Embed Size (px)
Citation preview
Chapter 2 A1 Glencoe Algebra 2
An
swer
s
Answers (Anticipation Guide and Lesson 2-1)
STEP
1
Cha
pter
23
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Ant
icip
atio
n G
uide
Lin
ear
Rel
atio
ns
and
Fu
nct
ion
s
Bef
ore
you
beg
in C
ha
pte
r 2
•R
ead
each
sta
tem
ent.
•D
ecid
e w
het
her
you
Agr
ee (
A)
or D
isag
ree
(D)
wit
h t
he
stat
emen
t.
•W
rite
Aor
D i
n t
he
firs
t co
lum
n O
R i
f yo
u a
re n
ot s
ure
wh
eth
er y
ou a
gree
or
disa
gree
,w
rite
NS
(N
ot S
ure
).
Aft
er y
ou c
omp
lete
Ch
ap
ter
2
•R
erea
d ea
ch s
tate
men
t an
d co
mpl
ete
the
last
col
um
n b
y en
teri
ng
an A
or a
D.
•D
id a
ny
of y
our
opin
ion
s ab
out
the
stat
emen
ts c
han
ge f
rom
th
e fi
rst
colu
mn
?
•F
or t
hos
e st
atem
ents
th
at y
ou m
ark
wit
h a
D, u
se a
pie
ce o
f pa
per
to w
rite
an
exa
mpl
e of
wh
y yo
u d
isag
ree.
STEP
2
ST
EP
1S
TE
P 2
A,D
,or
NS
Sta
tem
ent
A o
r D
1.A
fun
ctio
n i
s an
y se
t of
ord
ered
pai
rs.
D2.
If a
ver
tica
l li
ne
inte
rsec
ts t
he
grap
h o
f a
rela
tion
in
tw
o or
m
ore
poin
ts, t
hen
th
e re
lati
on i
s n
ot a
fu
nct
ion
.A
3.A
lin
ear
fun
ctio
n i
s a
fun
ctio
n w
hos
e or
dere
d pa
irs
sati
sfy
a li
nea
r eq
uat
ion
.A
4.T
he
slop
e of
a l
ine
is t
he
chan
ge o
f x-
coor
din
ates
div
ided
by
the
chan
ge o
f y-
coor
din
ates
.D
5.A
vert
ical
lin
e h
as a
n u
nde
fin
ed s
lope
.A
6.A
ny
two
perp
endi
cula
r li
nes
hav
e th
e sa
me
slop
e.D
7.A
lin
e w
ritt
en i
n t
he
form
y �
mx
�b
is s
aid
to b
e in
sl
ope-
inte
rcep
t fo
rm.
A
8.If
a l
ine
has
th
e eq
uat
ion
y�
3�
4(x
� 3
), t
hen
(�
2, �
3)
is a
poi
nt
on t
he
lin
e.
D
9.A
lin
e of
fit
for
th
e gr
aph
of
a se
t of
dat
a pa
sses
th
rou
gh
all
data
poi
nts
on
th
e gr
aph
.D
10.
Asc
atte
r pl
ot o
f a
data
set
sh
ows
if t
her
e is
a r
elat
ion
ship
be
twee
n t
he
data
.A
11.
Th
e gr
aph
of
a st
ep f
un
ctio
n c
onsi
sts
of l
ine
segm
ents
or
rays
th
at a
re n
ot c
onn
ecte
d.A
12.
Th
e gr
aph
of
y�
2x�
4 is
th
e sa
me
as t
he
grap
h o
f th
e li
ne
y�
2x�
4.D
Chapter Resources
2-1
Lesson 2-1
Cha
pter
25
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
Less
on R
eadi
ng G
uide
Rel
atio
ns
and
Fu
nct
ion
sG
et R
ead
y fo
r th
e Le
sso
nR
ead
th
e in
trod
uct
ion
to
Les
son
2-1
in
you
r te
xtb
ook
.
•R
efer
to
the
tabl
e. W
hat
doe
s th
e or
dere
d pa
ir (
8, 2
0) t
ell
you
?F
or
a d
eer,
the
aver
age
lon
gev
ity
is 8
yea
rs a
nd
th
e m
axim
um
lon
gev
ity
is 2
0 ye
ars.
•S
upp
ose
that
th
is t
able
is
exte
nde
d to
in
clu
de m
ore
anim
als.
Is
it p
ossi
ble
to h
ave
anor
dere
d pa
ir f
or t
he
data
in
wh
ich
th
e fi
rst
nu
mbe
r is
lar
ger
than
th
e se
con
d?S
amp
lean
swer
:N
o,t
he
max
imu
m lo
ng
evit
y m
ust
alw
ays
be
gre
ater
th
an t
he
aver
age
lon
gev
ity.
Rea
d t
he
Less
on
1.a.
Exp
lain
th
e di
ffer
ence
bet
wee
n a
rel
atio
n a
nd
a fu
nct
ion
.S
amp
le a
nsw
er:
Are
lati
on
is a
ny s
et o
f o
rder
ed p
airs
.A f
un
ctio
n is
a s
pec
ial k
ind
of
rela
tio
n in
wh
ich
eac
h e
lem
ent
of
the
do
mai
n is
pai
red
wit
h e
xact
lyo
ne
elem
ent
in t
he
ran
ge.
b.
Exp
lain
th
e di
ffer
ence
bet
wee
n d
omai
n a
nd
ran
ge.
Sam
ple
an
swer
:Th
e d
om
ain
of
a re
lati
on
is t
he
set
of
all f
irst
co
ord
inat
es o
f th
e o
rder
ed p
airs
.Th
era
ng
e is
th
e se
t o
f al
l sec
on
d c
oo
rdin
ates
.
2.a.
Wri
te t
he
dom
ain
an
d ra
nge
of
the
rela
tion
sh
own
in
th
e gr
aph
.
D:
{�3,
�2,
�1,
0,3}
;R
:{�
5,�
4,0,
1,2,
4}
b.
Is t
his
rel
atio
n a
fu
nct
ion
? E
xpla
in.
Sam
ple
an
swer
:N
o,i
t is
no
t a
fun
ctio
nb
ecau
se o
ne
of
the
elem
ents
of
the
do
mai
n,3
,is
pai
red
wit
h t
wo
elem
ents
of
the
ran
ge.
Rem
emb
er W
hat
Yo
u L
earn
ed
3.L
ook
up
the
wor
ds d
epen
den
tan
d in
dep
end
ent
in a
dic
tion
ary.
How
can
th
e m
ean
ing
ofth
ese
wor
ds h
elp
you
dis
tin
guis
h b
etw
een
in
depe
nde
nt
and
depe
nde
nt
vari
able
s in
afu
nct
ion
?S
amp
le a
nsw
er:T
he
vari
able
wh
ose
val
ues
dep
end
on
,or
are
det
erm
ined
by,
the
valu
es o
f th
e o
ther
var
iab
le is
th
e d
epen
den
t va
riab
le.
( 0, 4
)
( 3, 1
)
( 3, –
4)( –
1, –
5)
( –2,
0)
( –3,
2)
x
y
O
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A1
Chapter 2 A2 Glencoe Algebra 2
Answers (Lesson 2-1)
Exam
ple
Stud
y G
uide
and
Inte
rven
tion
Rel
atio
ns
and
Fu
nct
ion
s
Cha
pter
26
Gle
ncoe
Alg
ebra
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
Gra
ph
Rel
atio
ns
Are
lati
onca
n b
e re
pres
ente
d as
a s
et o
f or
dere
d pa
irs
or a
s an
equ
atio
n; t
he
rela
tion
is
then
th
e se
t of
all
ord
ered
pai
rs (
x, y
) th
at m
ake
the
equ
atio
n t
rue.
Th
e d
omai
nof
a r
elat
ion
is
the
set
of a
ll f
irst
coo
rdin
ates
of
the
orde
red
pair
s, a
nd
the
ran
geis
th
e se
t of
all
sec
ond
coor
din
ates
.A
fun
ctio
nis
a r
elat
ion
in
wh
ich
eac
h e
lem
ent
of t
he
dom
ain
is
pair
ed w
ith
exa
ctly
on
eel
emen
t of
th
e ra
nge
. You
can
tel
l if
a r
elat
ion
is
a fu
nct
ion
by
grap
hin
g, t
hen
usi
ng
the
vert
ical
lin
e te
st. I
f a
vert
ical
lin
e in
ters
ects
th
e gr
aph
at
mor
e th
an o
ne
poin
t, t
he
rela
tion
is
not
a f
un
ctio
n.
Gra
ph
th
e eq
uat
ion
y�
2x�
3 an
d f
ind
th
e d
omai
n a
nd
ran
ge. I
sth
e eq
uat
ion
dis
cret
e or
con
tin
uou
s? D
oes
the
equ
atio
n r
epre
sen
t a
fun
ctio
n?
Mak
e a
tabl
e of
val
ues
to
fin
d or
dere
d pa
irs
that
sa
tisf
y th
e eq
uat
ion
. Th
en g
raph
th
e or
dere
d pa
irs.
Th
e do
mai
n a
nd
ran
ge a
re b
oth
all
rea
l n
um
bers
. Th
eeq
uat
ion
can
be
grap
hed
by
lin
e, s
o it
is
con
tin
uou
s. T
he
grap
h p
asse
s th
e ve
rtic
al l
ine
test
, so
it i
s a
fun
ctio
n.
Gra
ph
eac
h r
elat
ion
or
equ
atio
n a
nd
fin
d t
he
dom
ain
an
d r
ange
. Nex
t d
eter
min
e if
the
rela
tion
is
dis
cret
e or
con
tin
uou
s. T
hen
det
erm
ine
wh
eth
er t
he
rela
tion
or
equ
atio
n i
s a
fun
ctio
n.
1.{(
1, 3
), (
�3,
5),
2.{(
3, �
4), (
1, 0
),
3.{(
0, 4
), (
�3,
�2)
,
(�2,
5),
(2,
3)}
(2, �
2), (
3, 2
)}(3
, 2),
(5,
1)}
D �
{�3,
�2,
1,2}
,D
�{1
,2,3
},D
�{�
3,0,
3,5}
,R
�{3
,5};
R �
{�4,
�2,
0,2}
;R
�{�
2,1,
2,4}
;d
iscr
ete;
yes
dis
cret
e;n
od
iscr
ete;
yes
4.y
�x2
�1
5.y
�x
�4
6.y
�3x
�2
D �
all r
eals
,D
�al
l rea
ls,
D �
all r
eals
,R
�{y
⏐y�
�1}
;R
�al
l rea
ls;
R �
all r
eals
;co
nti
nu
ou
s;ye
sco
nti
nu
ou
s;ye
sco
nti
nu
ou
s;ye
sx
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
xy
�1
�5
0�
3
1�
1
21
33
Exer
cise
s
Lesson 2-1
Equ
atio
ns
of
Fun
ctio
ns
and
Rel
atio
ns
Equ
atio
ns
that
rep
rese
nt
fun
ctio
ns
are
ofte
n w
ritt
en i
n f
un
ctio
nal
not
atio
n. F
or e
xam
ple,
y�
10 �
8xca
n b
e w
ritt
en a
s f(
x) �
10 �
8x. T
his
not
atio
n e
mph
asiz
es t
he
fact
th
at t
he
valu
es o
f y,
th
e d
epen
den
tva
riab
le, d
epen
d on
th
e va
lues
of
x, t
he
ind
epen
den
t va
riab
le.
To e
valu
ate
a fu
nct
ion
, or
fin
d a
fun
ctio
nal
val
ue,
mea
ns
to s
ubs
titu
te a
giv
en v
alu
e in
th
edo
mai
n i
nto
th
e eq
uat
ion
to
fin
d th
e co
rres
pon
din
g el
emen
t in
th
e ra
nge
.
Giv
en t
he
fun
ctio
n f
(x)
�x2
�2x
, fin
d e
ach
val
ue.
a.f(
3)
f(x)
�x2
�2x
Orig
inal
fun
ctio
n
f(3)
�32
�2(
3)S
ubst
itute
.
�15
Sim
plify
.
b.
f(5a
)
f(x)
�x2
�2x
Orig
inal
fun
ctio
n
f(5a
) �
(5a)
2�
2(5a
)S
ubst
itute
.
�25
a2�
10a
Sim
plify
.
Fin
d e
ach
val
ue
if f
(x)
��
2x�
4.
1.f(
12)
�20
2.f(
6)�
83.
f(2b
)�
4b�
4
Fin
d e
ach
val
ue
if g
(x)
�x3
�x.
4.g(
5)12
05.
g(�
2)�
66.
g(7c
)34
3c3
�7c
Fin
d e
ach
val
ue
if f
(x)
�2x
�an
d g
(x)
�0.
4x2
�1.
2.
7.f(
0.5)
58.
f(�
8)�
169.
g(3)
2.4
10.g
(�2.
5)1.
311
.f(4
a)8a
�12
.g�
��
1.2
13.f
��6
14.g
(10)
38.8
15.f
(200
)40
0.01
Let
f(x
) �
2x2
�1.
16.F
ind
the
valu
es o
f f(
2) a
nd
f(5)
.f(
2) �
7,f(
5) �
49
17.C
ompa
re t
he
valu
es o
f f(
2) �
f(5)
an
d f(
2 �
5).
f(2)
�f(
5) �
343,
f(2
�5)
�19
9
2 � 31 � 3
b2
� 10b � 2
1 � 2a1 � 4
2 � x
Stud
y G
uide
and
Inte
rven
tion
(co
ntin
ued)
Rel
atio
ns
and
Fu
nct
ion
s
Cha
pter
27
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
Exam
ple
Exer
cise
s
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A2
Chapter 2 A3 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-1)
Cha
pter
28
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceR
elat
ion
s an
d F
un
ctio
ns
Det
erm
ine
wh
eth
er e
ach
rel
atio
n i
s a
fun
ctio
n. W
rite
yes
or n
o.
1.ye
s2.
no
3.ye
s4.
no
Gra
ph
eac
h r
elat
ion
or
equ
atio
n a
nd
fin
d t
he
dom
ain
an
d r
ange
. Nex
t d
eter
min
e if
the
rela
tion
is
dis
cret
e or
con
tin
uou
s. T
hen
det
erm
ine
wh
eth
er t
he
rela
tion
or
equ
atio
n i
s a
fun
ctio
n.
5.{(
2, �
3), (
2, 4
), (
2, �
1)}
6.{(
2, 6
), (
6, 2
)}
D �
{2},
R �
{�3,
�1,
4};
dis
cret
e;n
oD
�{2
,6},
R �
{2,6
};d
iscr
ete;
yes
7.{(
�3,
4),
(�
2, 4
), (
�1,
�1)
, (3,
�1)
}8.
x�
�2
D �
{�3,
�2,
�1,
3},
D �
{�2}
,R �
all r
eals
;dis
cret
e;n
o
R �
{�1,
4};
dis
cret
e;ye
s
Fin
d e
ach
val
ue
if f
(x)
�2x
�1
and
g(x
) �
2 �
x2.
9.f(
0)�
110
.f(1
2)23
11.g
(4)
�14
12.f
(�2)
�5
13.g
(�1)
114
.f(d
)2d
�1
x
y
O
( –2,
4)
( –3,
4)
( –1,
–1)
( 3, –
1)x
y
O
( 2, 6
) ( 6, 2
)
x
y
O
( 2, 4
)
( 2, –
1)
( 2, –
3)
x
y
O
x
y
O
xy
12
24
36
31 5
Dom
ain
Rang
e
100
200
300
50 100
150
Dom
ain
Rang
e
2-1
Lesson 2-1
Det
erm
ine
wh
eth
er e
ach
rel
atio
n i
s a
fun
ctio
n. W
rite
yes
or n
o.
1.n
o2.
yes
3.ye
s4.
no
Gra
ph
eac
h r
elat
ion
or
equ
atio
n a
nd
fin
d t
he
dom
ain
an
d r
ange
. Nex
t d
eter
min
e if
the
rela
tion
is
dis
cret
e or
con
tin
uou
s. T
hen
det
erm
ine
wh
eth
er t
he
rela
tion
or
equ
atio
n i
s a
fun
ctio
n.
5.{(
�4,
�1)
, (4,
0),
(0,
3),
(2,
0)}
6.y
�2x
�1
D �
{�4,
0,2,
4},
D �
all r
eals
,R �
all r
eals
;R
�{�
1,0,
3};
dis
cret
e;ye
sco
nti
nu
ou
s;ye
s
Fin
d e
ach
val
ue
if f
(x)
�an
d g
(x)
��
2x�
3.
7.f(
3)1
8.f(
�4)
�9.
g ��2
10.f
(�2)
un
def
ined
11.g
(�6)
1512
.f(m
�2)
13.M
USI
CT
he
orde
red
pair
s (1
, 16)
, (2,
16)
, (3,
32)
, (4,
32)
, an
d (5
, 48)
rep
rese
nt
the
cost
of
buyi
ng
vari
ous
nu
mbe
rs o
f C
Ds
thro
ugh
a m
usi
c cl
ub.
Ide
nti
fy t
he
dom
ain
an
d ra
nge
of
the
rela
tion
. Is
the
rela
tion
dis
cret
e or
con
tin
uou
s? I
s th
e re
lati
on a
fu
nct
ion
?D
�{1
,2,3
,4,5
},R
�{1
6,32
,48}
;d
iscr
ete;
yes
14.C
OM
PUTI
NG
If a
com
pute
r ca
n d
o on
e ca
lcu
lati
on i
n 0
.000
0000
015
seco
nd,
th
en t
he
fun
ctio
n T
(n)
�0.
0000
0000
15n
give
s th
e ti
me
requ
ired
for
th
e co
mpu
ter
to d
o n
calc
ula
tion
s. H
ow l
ong
wou
ld i
t ta
ke t
he
com
pute
r to
do
5 bi
llio
n c
alcu
lati
ons?
7.5
s
5 � m
1 � 25 � 2
5� x
�2
x
y
O
( –4,
–1)
( 2, 0
)
( 0, 3
)
( 4, 0
) x
y
O
x
y
O
xy
�3
0
�1
�1
00
2�
2
34
5 10 15
105
110
Dom
ain
Rang
e
2 8
21 25 30
Dom
ain
Rang
e
Prac
tice
R
elat
ion
s an
d F
un
ctio
ns
Cha
pter
29
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A3
Chapter 2 A4 Glencoe Algebra 2
Answers (Lesson 2-1)
1.PL
AN
ETS
Th
e ta
ble
belo
w g
ives
th
em
ean
dis
tan
ce f
rom
th
e S
un
an
d or
bita
lpe
riod
of
the
nin
e m
ajor
pla
net
s in
ou
rS
olar
Sys
tem
. Th
ink
of t
he
mea
ndi
stan
ce a
s th
e do
mai
n a
nd
the
orbi
tal
peri
od a
s th
e ra
nge
of
a re
lati
on. I
s th
isre
lati
on a
fu
nct
ion
? E
xpla
in.
Yes,
it is
a f
un
ctio
n b
ecau
seev
ery
valu
e in
th
e d
om
ain
co
rres
po
nd
s to
a s
ing
le v
alu
e in
th
e ra
ng
e.
2.PR
OB
AB
ILIT
YM
arth
a ro
lls
a n
um
ber
cube
sev
eral
tim
es a
nd
mak
es t
he
freq
uen
cy g
raph
sh
own
. Wri
te a
rel
atio
nto
rep
rese
nt
this
dat
a.
{(1,
4),(
2,3)
,(3,
6),(
4,3)
,(5,
5),(
6,4)
}
3.SC
HO
OL
Th
e n
um
ber
of s
tude
nts
Nin
Vas
sia’
s sc
hoo
l is
giv
en b
y N
= 12
0 +
30G
, wh
ere
G i
s th
e gr
ade
leve
l. Is
285
in t
he
ran
ge o
f th
is f
un
ctio
n?
No
.If
N�
285,
then
G�
5.5,
but
gra
de
leve
ls a
re in
teg
ers
so28
5 is
no
t in
th
e ra
ng
e o
f th
efu
nct
ion
.
4.FL
OW
ERS
An
thon
y de
cide
s to
dec
orat
ea
ball
room
wit
h r
= 3n
+ 20
ros
es, w
her
en
is t
he
nu
mbe
r of
dan
cers
. It
occu
rs t
oA
nth
ony
that
th
e da
nce
rs a
lway
s co
me
in p
airs
. Th
at i
s, n
= 2p
, wh
ere
pis
th
en
um
ber
of p
airs
. Wh
at i
s r
as a
fu
nct
ion
of p
? r
�6p
�20
SALE
SF
or E
xerc
ises
5–7
, use
th
efo
llow
ing
info
rmat
ion
.
Coo
l Ath
leti
cs in
trod
uced
the
new
Pow
erS
neak
er in
one
of
thei
r st
ores
. The
tab
lesh
ows
the
sale
s fo
r th
e fi
rst
6 w
eeks
.
5.G
raph
th
e da
ta.
6.Id
enti
fy t
he
dom
ain
an
d ra
nge
.d
om
ain
:{1
,2,3
,4,5
,6}
ran
ge:
{8,1
0,15
,22,
31,4
4}
7.Is
th
e re
lati
on a
fu
nct
ion
? E
xpla
in.
Yes,
it is
a f
un
ctio
n b
ecau
seev
ery
valu
e in
th
e d
om
ain
co
rres
po
nd
s to
a s
ing
le v
alu
e in
th
e ra
ng
e.
Pairs Sold
1015 5 0202530354045
Wee
k3
21
57
46
Frequency
23 1 04567
Nu
mb
er3
21
54
6
Wor
d Pr
oble
m P
ract
ice
R
elat
ion
s an
d F
un
ctio
ns
Cha
pter
210
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Pla
net
Mea
n D
ista
nce
fro
m
Orb
ital
Per
iod
Su
n (
AU
)(y
ears
)
Mer
cury
0.38
70.
241
Ven
us
0.72
30.
615
Ear
th
1.0
1.0
Mar
s 1.
524
1.88
1
Jupi
ter
5.20
4 11
.75
Sat
urn
9.58
2 29
.5
Ura
nus
19.2
01
84
Nep
tune
30
.047
16
5
Plu
to
39.2
36
248
Wee
k1
23
45
6
Pai
rs S
old
810
1522
3144
Lesson 2-1
Cha
pter
211
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
Map
pin
gs
Th
ere
are
thre
e sp
ecia
l w
ays
in w
hic
h o
ne
set
can
be
map
ped
to a
not
her
. A
map
pin
g ca
n b
e on
e-to
-on
e, o
nto
, bij
ecti
ve, o
r n
one
of t
hes
e.
Sta
te w
het
her
eac
h m
app
ing
is o
ne-
to-o
ne,
on
to, b
ijec
tive
, or
non
e of
th
ese.
1.2.
3.4.
on
too
ne-
to-o
ne
bije
ctiv
eo
nto
5.6.
7.8.
no
ne
on
ton
on
eb
iject
ive
9.C
an a
set
be
map
ped
onto
a se
t w
ith
few
er e
lem
ents
th
an i
t h
as?
yes
10.C
an a
set
hav
e a
one-
to-o
ne
map
pin
g in
to a
set
th
at h
as m
ore
elem
ents
th
an i
t h
as?
yes
11.I
f a
map
pin
g fr
om s
et A
into
set
Bis
bij
ecti
ve, w
hat
can
you
con
clu
de
abou
t th
e n
um
ber
of e
lem
ents
in
Aan
d B
?T
he
sets
hav
e th
e sa
me
nu
mb
er o
f el
emen
ts.
1 4�
7 0
�2 9 12 5
Dom
ain
Rang
e
1 4�
7 0
�2 9 12 5
Dom
ain
Rang
e
15 10 2�
3
Dom
ain
Rang
e
1 4�
7 0
�2 9 12 5
Dom
ain
Rang
e
3
10 �6 24 2
Dom
ain
Rang
e
a g k l q
1 3 7 9�
5
Dom
ain
Rang
e
4 12 6
0�
3 9 7
Dom
ain
Rang
e
2 4�
1�
4
7 0 2
Dom
ain
Rang
e
On
e-to
-on
eA
map
ping
fro
m s
et A
to s
et B
whe
re d
iffer
ent
elem
ents
of
Aar
e ne
ver
map
ped
to t
he
map
pin
gsa
me
elem
ent
of B
.
On
to m
app
ing
Am
appi
ng f
rom
set
Ato
set
Bw
here
eac
h el
emen
t of
set
Bha
s at
leas
t on
e el
emen
t of
se
t A
map
ped
to it
.
Bije
ctiv
e A
map
ping
fro
m s
et A
onto
set
Bth
at is
one
-to-
one
and
onto
.m
app
ing
Enri
chm
ent
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A4
Chapter 2 A5 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-2)
Cha
pter
212
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 2
-2 i
n y
our
text
boo
k.
•If
Lol
ita
spen
ds 2
hou
rs s
tudy
ing
mat
h, h
ow m
any
hou
rs w
ill
she
hav
e
to s
tudy
ch
emis
try?
1h
ou
rs•
Su
ppos
e th
at L
olit
a de
cide
s to
sta
y u
p on
e h
our
late
r so
th
at s
he
now
has
5 h
ours
to
stu
dy a
nd
do h
omew
ork.
Wri
te a
lin
ear
equ
atio
n t
hat
des
crib
es t
his
sit
uat
ion
.x
�y
�5
Rea
d t
he
Less
on
1.W
rite
yes
or n
oto
tel
l w
het
her
eac
h l
inea
r eq
uat
ion
is
in s
tan
dard
for
m. I
f it
is
not
,ex
plai
n w
hy
it i
s n
ot.
a.�
x�
2y�
5N
o;
Ais
neg
ativ
e.
b.
9x�
12y
��
5ye
s
c.5x
�7y
�3
yes
d.
2x�
y�
1N
o;
Bis
no
t an
inte
ger
.
e.0x
�0y
�0
No
;A
and
Bar
e b
oth
0.
f.2x
�4y
�8
No
;Th
e g
reat
est
com
mo
n f
acto
r o
f 2,
4,an
d 8
is 2
,no
t 1.
2.H
ow c
an y
ou u
se t
he
stan
dard
for
m o
f a
lin
ear
equ
atio
n t
o te
ll w
het
her
th
e gr
aph
is
ah
oriz
onta
l li
ne
or a
ver
tica
l li
ne?
If A
�0,
then
th
e g
rap
h is
a h
ori
zon
tal l
ine.
IfB
�0,
then
th
e g
rap
h is
a v
erti
cal l
ine.
Rem
emb
er W
hat
Yo
u L
earn
ed
3.O
ne
way
to
rem
embe
r so
met
hin
g is
to
expl
ain
it
to a
not
her
per
son
. Su
ppos
e th
at y
ou
are
stu
dyin
g th
is l
esso
n w
ith
a f
rien
d w
ho
thin
ks t
hat
sh
e sh
ould
let
x�
0 to
fin
d th
e x-
inte
rcep
t an
d le
t y
�0
to f
ind
the
y-in
terc
ept.
How
wou
ld y
ou e
xpla
in t
o h
er h
ow t
ore
mem
ber
the
corr
ect
way
to
fin
d in
terc
epts
of
a li
ne?
Sam
ple
an
swer
:Th
e x-
inte
rcep
t is
th
e x-
coo
rdin
ate
of
a p
oin
t o
n t
he
x-ax
is.E
very
po
int
on
th
e x-
axis
has
y-c
oo
rdin
ate
0,so
let
y�
0 to
fin
d a
n x
-in
terc
ept.
Th
e y-
inte
rcep
t is
th
e y-
coo
rdin
ate
of
a p
oin
t o
n t
he
y-ax
is.E
very
po
int
on
th
e y-
axis
has
x-c
oo
rdin
ate
0,so
let
x�
0 to
fin
d a
y-i
nte
rcep
t.
4 � 7
1 � 2
1 � 2
Less
on R
eadi
ng G
uide
Lin
ear
Eq
uat
ion
s
Exer
cise
s
Exam
ple
3
Exam
ple
2
Lesson 2-2
Iden
tify
Lin
ear
Equ
atio
ns
and
Fu
nct
ion
sA
lin
ear
equ
atio
nh
as n
o op
erat
ion
sot
her
th
an a
ddit
ion
, su
btra
ctio
n, a
nd
mu
ltip
lica
tion
of
a va
riab
le b
y a
con
stan
t. T
he
vari
able
s m
ay n
ot b
e m
ult
ipli
ed t
oget
her
or
appe
ar i
n a
den
omin
ator
. Ali
nea
r eq
uat
ion
doe
sn
ot c
onta
in v
aria
bles
wit
h e
xpon
ents
oth
er t
han
1. T
he
grap
h o
f a
lin
ear
equ
atio
n i
s a
lin
e.
Ali
nea
r fu
nct
ion
is a
fu
nct
ion
wh
ose
orde
red
pair
s sa
tisf
y a
lin
ear
equ
atio
n. A
ny
lin
ear
fun
ctio
n c
an b
e w
ritt
en i
n t
he
form
f(x
) �
mx
�b,
wh
ere
man
d b
are
real
nu
mbe
rs.
If a
n e
quat
ion
is
lin
ear,
you
nee
d on
ly t
wo
poin
ts t
hat
sat
isfy
th
e eq
uat
ion
in
ord
er t
o gr
aph
the
equ
atio
n. O
ne
way
is
to f
ind
the
x-in
terc
ept
and
the
y-in
terc
ept
and
con
nec
t th
ese
two
poin
ts w
ith
a l
ine.
Cha
pter
213
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
Fin
d t
he
x-in
terc
ept
and
the
y-in
terc
ept
of t
he
grap
h o
f 4x
�5y
�20
.T
hen
gra
ph
th
e eq
uat
ion
.
Th
e x-
inte
rcep
t is
th
e va
lue
of x
wh
en y
�0.
4x�
5y�
20O
rigin
al e
quat
ion
4x�
5(0)
�20
Sub
stitu
te 0
for
y.
x�
5S
impl
ify.
So
the
x-in
terc
ept
is 5
.S
imil
arly
, th
e y-
inte
rcep
t is
�4.
x
y
O
Sta
te w
het
her
eac
h e
qu
atio
n o
r fu
nct
ion
is
lin
ear.
Wri
te y
esor
no.
If
no,
exp
lain
.
1.6y
�x
�7
yes
2.9x
�N
o;
the
3.f(
x) �
2 �
yes
vari
able
yap
pea
rs
in t
he
den
om
inat
or.
Fin
d t
he
x-in
terc
ept
and
th
e y-
inte
rcep
t of
th
e gr
aph
of
each
eq
uat
ion
. Th
en g
rap
hth
e eq
uat
ion
.
4.2x
�7y
�14
5.5y
�x
�10
6.2.
5x�
5y�
7.5
�0
x-in
t:7;
y-in
t:2
x-in
t:�
10;
y-in
t:2
x-in
t:�
3;y-
int:
1.5
x
y
Ox
y
Ox
y
O
x � 1118 � y
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Is f
(x)
�0.
2 �
ali
nea
r fu
nct
ion
? E
xpla
in.
Yes;
it
is a
lin
ear
fun
ctio
n b
ecau
se i
t ca
nbe
wri
tten
in
th
e fo
rmf(
x) �
�x
�0.
2. Is 2
x�
xy�
3y�
0 a
lin
ear
fun
ctio
n?
Exp
lain
.
No;
it
is n
ot a
lin
ear
fun
ctio
n b
ecau
se t
he
vari
able
s x
and
yar
e m
ult
ipli
ed t
oget
her
in t
he
mid
dle
term
.
1 � 5
x � 5Ex
amp
le 1
Stud
y G
uide
and
Inte
rven
tion
Lin
ear
Eq
uat
ion
s
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A5
Chapter 2 A6 Glencoe Algebra 2
Answers (Lesson 2-2)
Stan
dar
d F
orm
Th
e st
and
ard
for
mof
a l
inea
r eq
uat
ion
is
Ax
�B
y�
C, w
her
e A
, B, a
nd
Car
e in
tege
rs w
hos
e gr
eate
st c
omm
on f
acto
r is
1.
Wri
te e
ach
eq
uat
ion
in
sta
nd
ard
for
m. I
den
tify
A, B
, an
d C
.
Stud
y G
uide
and
Inte
rven
tion
(co
ntin
ued)
Lin
ear
Eq
uat
ion
s
a.y
�8x
�5
y�
8x�
5O
rigin
al e
quat
ion
�8x
�y
��
5S
ubtr
act
8xfr
om e
ach
side
.
8x�
y�
5M
ultip
ly e
ach
side
by
�1.
So
A�
8, B
��
1, a
nd
C�
5.
b.
14x
��
7y�
21
14x
��
7y�
21O
rigin
al e
quat
ion
14x
�7y
�21
Add
7y
to e
ach
side
.
2x�
y�
3D
ivid
e ea
ch s
ide
by 7
.
So
A�
2, B
�1,
an
d C
�3.
Wri
te e
ach
eq
uat
ion
in
sta
nd
ard
for
m. I
den
tify
A, B
, an
d C
.
1.2x
�4y
�1
2.5y
�2x
�3
3.3x
��
5y�
22x
�4y
��
1;A
�2,
2x�
5y�
�3;
A�
2,3x
�5y
�2;
A�
3,B
��
4,C
��
1B
��
5,C
��
3B
�5,
C�
2
4.18
y�
24x
�9
5.y
�x
�5
6.6y
�8x
�10
�0
8x�
6y�
3;A
�8,
8x�
9y�
�60
;A
�8,
4x�
3y�
5;A
�4,
B�
�6,
C�
3B
��
9,C
��
60
B�
�3,
C�
5
7.0.
4x�
3y�
108.
x�
4y�
79.
2y�
3x�
62x
�15
y�
50;
A�
2,x
�4y
��
7;A
�1,
3x�
2y�
�6;
A�
3,B
�15
,C�
50B
��
4,C
��
7 B
��
2,C
��
6
10.
x�
y�
2 �
011
.4y
�4x
�12
�0
12.3
x�
�18
6x�
5y�
30;
A�
6,x
�y
��
3;A
�1,
x�
�6;
A�
1,B
�5,
C�
30B
�1,
C�
�3
B�
0,C
��
6
13.x
��
714
.3y
�9x
�18
15.2
x�
20 �
8y
9x�
y�
63;
A�
9,3x
�y
�6;
A�
3,x
�4y
�10
;A
�1,
B �
�1,
C�
63B
��
1,C
�6
B�
4,C
�10
16.
�3
�2x
17. �
��y
�8
18.0
.25y
�2x
�0.
75
8x�
y�
�12
;A
�8,
10x
�3y
�32
;A
�10
,8x
�y
�3;
A�
8,B
��
1,C
��
12B
��
3,C
�32
B�
�1,
C�
3
19.2
y��
4 �
020
.1.6
x�
2.4y
�4
21.0
.2x
�10
0 �
0.4y
x�
12y
��
24;
A�
1,2x
�3y
�5;
A�
2,x
�2y
�50
0;A
�1,
B�
�12
,C �
�24
B�
�3,
C�
5 B
�2,
C �
500
x � 6
3 � 45x � 2
y � 4
y � 9
1 � 32 � 5
2 � 33 � 4
Cha
pter
214
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exam
ple
Exer
cise
s
Skill
s Pr
acti
ceL
inea
r E
qu
atio
ns
2-2
Lesson 2-2
Sta
te w
het
her
eac
h e
qu
atio
n o
r fu
nct
ion
is
lin
ear.
Wri
te y
esor
no.
If
no,
exp
lain
you
r re
ason
ing.
1.y
�3x
2.y
��
2 �
5x
yes
yes
3.2x
�y
�10
4.f(
x) �
4x2
yes
No
;th
e ex
po
nen
t o
f x
is n
ot
1.
5.�
�y
�15
6.x
�y
�8
No
;x
is in
a d
eno
min
ato
r.ye
s
7.g(
x) �
88.
h(x
) �
�x��
3
yes
No
;x
is in
sid
e a
squ
are
roo
t.
Wri
te e
ach
eq
uat
ion
in
sta
nd
ard
for
m. I
den
tify
A, B
, an
d C
.
9.y
�x
x�
y�
0;1,
�1,
010
.y�
5x�
15x
�y
��
1;5,
�1,
�1
11.2
x�
4 �
7y2x
�7y
�4;
2,7,
412
.3x
��
2y�
23x
�2y
��
2;3,
2,�
2
13.5
y�
9 �
05y
�9;
0,5,
914
.�6y
�14
�8x
4x�
3y�
7;4,
3,7
Fin
d t
he
x-in
terc
ept
and
th
e y-
inte
rcep
t of
th
e gr
aph
of
each
eq
uat
ion
. Th
en g
rap
hth
e eq
uat
ion
.
15.y
�3x
�6
2,�
616
.y�
�2x
0,0
17.x
�y
�5
5,5
18.2
x�
5y�
105,
2
( 5, 0
)
( 0, 2
)
x
y
O( 5
, 0)
( 0, 5
)
x
y
O
( 0, 0
)x
y
O
( 2, 0
)
( 0, –
6)
x
y
O
1 � 33 � x
Cha
pter
215
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A6
Chapter 2 A7 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-2)
Sta
te w
het
her
eac
h e
qu
atio
n o
r fu
nct
ion
is
lin
ear.
Wri
te y
esor
no.
If
no,
exp
lain
you
r re
ason
ing.
1.h
(x)
�23
yes
2.y
�x
yes
3.y
�N
o;
xis
a d
eno
min
ato
r.4.
9 �
5xy
�2
No
;x
and
yar
e m
ult
iplie
d.
Wri
te e
ach
eq
uat
ion
in
sta
nd
ard
for
m. I
den
tify
A, B
, an
d C
.
5.y
�7x
�5
7x�
y�
5;7,
�1,
56.
y�
x�
5 3x
�8y
��
40;3
,�8,
�40
7.3y
�5
�0
3y�
5;0,
3,5
8.x
��
y�
28x
�8y
�21
;28
,8,2
1
Fin
d t
he
x-in
terc
ept
and
th
e y-
inte
rcep
t of
th
e gr
aph
of
each
eq
uat
ion
. Th
en g
rap
hth
e eq
uat
ion
.
9.y
�2x
�4
�2,
410
.2x
�7y
�14
7,2
11.y
��
2x�
4�
2,�
412
.6x
�2y
�6
1,3
13.M
EASU
RE
Th
e eq
uat
ion
y�
2.54
xgi
ves
the
len
gth
in
cen
tim
eter
s co
rres
pon
din
g to
ale
ngt
h x
in i
nch
es. W
hat
is
the
len
gth
in
cen
tim
eter
s of
a 1
-foo
t ru
ler?
30.4
8 cm
LON
G D
ISTA
NC
EF
or E
xerc
ises
14
and
15,
use
th
e fo
llow
ing
info
rmat
ion
.
For
Meg
’s l
ong-
dist
ance
cal
lin
g pl
an, t
he
mon
thly
cos
t C
in d
olla
rs i
s gi
ven
by
the
lin
ear
fun
ctio
n C
(t)
�6
�0.
05t,
wh
ere
tis
th
e n
um
ber
of m
inu
tes
talk
ed.
14.W
hat
is
the
tota
l co
st o
f ta
lkin
g 8
hou
rs?
of t
alki
ng
20 h
ours
?$3
0;$6
6
15.W
hat
is
the
effe
ctiv
e co
st p
er m
inu
te (
the
tota
l co
st d
ivid
ed b
y th
e n
um
ber
of m
inu
tes
talk
ed)
of t
alki
ng
8 h
ours
? of
tal
kin
g 20
hou
rs?
$0.0
625;
$0.0
55
x
y
O( 1
, 0)
( 0, 3
)x
y
O(–
2, 0
)
( 0, –
4)
( 7, 0
)
( 0, 2
)
x
y
O( –
2, 0
)
( 0, 4
)
x
y
O
3 � 42 � 7
3 � 8
5 � x
2 � 3
Prac
tice
L
inea
r E
qu
atio
ns
Cha
pter
216
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 2-2
Wor
d Pr
oble
m P
ract
ice
Lin
ear
Eq
uat
ion
s
Cha
pter
217
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
1.W
OR
K R
ATE
Th
e li
nea
r eq
uat
ion
n
= 10
tde
scri
bes
n, t
he
nu
mbe
r of
orig
ami
boxe
s th
at H
olly
can
fol
d in
t
hou
rs. H
ow m
any
boxe
s ca
n H
olly
fo
ld i
n 3
hou
rs?
30 b
oxes
2.B
ASK
ETB
ALL
Ton
y to
ssed
a b
aske
tbal
l.B
elow
is
a gr
aph
sh
owin
g th
e h
eigh
t of
the
bask
etba
ll a
s a
fun
ctio
n o
f ti
me.
Is
this
th
e gr
aph
of
a li
nea
r fu
nct
ion
?E
xpla
in.
No
,it
is n
ot
linea
r b
ecau
seg
rap
hs
of
linea
r fu
nct
ion
s ar
eal
way
s st
raig
ht
lines
.Th
is g
rap
hcu
rves
.
3.PR
OFI
TP
aul
char
ges
peop
le $
25 t
o te
st t
he
air
qual
ity
in t
hei
r h
omes
. T
he
devi
ce h
e u
ses
to t
est
air
qual
ity
cost
him
$50
0. W
rite
an
equ
atio
n t
hat
desc
ribe
s P
aul’s
net
pro
fit
as a
fu
nct
ion
of t
he
nu
mbe
r of
cli
ents
he
gets
. How
man
y cl
ien
ts d
oes
he
nee
d to
bre
akev
en?
Pau
l’s p
rofi
t is
p�
25c
�50
0,if
c
is t
he
nu
mb
er o
f cl
ien
ts a
nd
pis
his
pro
fit.
He
nee
ds
20 c
lien
tsto
bre
ak e
ven
.
4.R
AM
PA
ram
p is
des
crib
ed b
y th
eeq
uat
ion
5x
�7y
�35
. Wh
at i
s th
e ar
eaof
th
e sh
aded
reg
ion
?
17.5
sq
uar
e u
nit
s
SWIM
MIN
G P
OO
LF
or E
xerc
ises
5–7
,u
se t
he
foll
owin
g in
form
atio
n.
Asw
imm
ing
pool
is
shap
ed a
s sh
own
bel
ow.
Th
e to
tal
peri
met
er i
s 11
0 fe
et.
5.W
rite
an
equ
atio
n t
hat
rel
ates
xan
d y.
Sam
ple
an
swer
:2x
�2y
�10
�11
0
6.W
rite
th
e li
nea
r eq
uat
ion
fro
m E
xerc
ise
5 in
sta
nda
rd f
orm
.x
�y
�50
7.G
raph
th
e eq
uat
ion
.
y
xO50 40 30 20 1080 70 60
5040
3020
1060
7080
x ft
y ft
5 ft
10 fty
xO
5x �
7y
� 3
5
Height (ft)
46 2810
Tim
e (s
)0.
60.
21.
0
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A7
Chapter 2 A8 Glencoe Algebra 2
Answers (Lessons 2-2 and 2-3)
Dio
ph
anti
ne
Eq
uat
ion
sT
he f
irst
gre
at a
lgeb
rais
t, D
ioph
antu
s of
Ale
xand
ria
(abo
ut A
.D. 3
00),
devo
ted
muc
h of
his
wor
k to
the
sol
ving
of
inde
term
inat
e eq
uati
ons.
A
n in
dete
rmin
ate
equa
tion
has
mor
e th
an o
ne v
aria
ble
and
an
unli
mit
ed n
umbe
r of
sol
utio
ns. A
n ex
ampl
e is
x�
2y�
4.
Whe
n th
e co
effi
cien
ts o
f an
inde
term
inat
e eq
uati
on a
re in
tege
rs a
nd
you
are
aske
d to
fin
d so
luti
ons
that
mus
t be
inte
gers
, the
equ
atio
n is
ca
lled
a d
ioph
anti
ne. S
uch
equa
tion
s ca
n be
qui
te d
iffi
cult
to
solv
e,
ofte
n in
volv
ing
tria
l and
err
or—
and
som
e lu
ck!
Sol
ve e
ach
dio
ph
anti
ne
equ
atio
n b
y fi
nd
ing
at l
east
on
e p
air
of p
osit
ive
inte
gers
th
at m
akes
th
e eq
uat
ion
tru
e. S
ome
hin
ts a
re g
iven
to
hel
p y
ou.
1.2x
�5y
�32
a.F
irst
sol
ve t
he
equ
atio
n f
or x
.x
�16
��5 2y �
b.
Wh
y m
ust
ybe
an
eve
n n
um
ber?
If y
is o
dd
,th
en x
is n
ot
an in
teg
er.
c.F
ind
at l
east
on
e so
luti
on.
Sam
ple
an
swer
s:(1
1,2)
,(6,
4),(
1,6)
2.5x
�2y
�42
a.F
irst
sol
ve t
he
equ
atio
n f
or x
.x
��42
� 52y
�
b.
Rew
rite
you
r an
swer
in
th
e fo
rm x
�8
�so
me
expr
essi
on.
x�
8 �
�2� 5
2y �
c.W
hy
mu
st (
2 �
2y)
be a
mu
ltip
le o
f 5?
So
th
at x
is a
n in
teg
er
d.
Fin
d at
lea
st o
ne
solu
tion
.S
amp
le a
nsw
ers:
(8,1
),(6
,6),
(4,1
1),(
2,16
)
3.2x
�7y
�29
4.7x
�5y
�11
8(1
1,1)
or
(4,3
)(1
4,4)
,(9,
11)
or
(4,1
8)
5.8x
�13
y�
100
6.3x
�4y
�22
(19,
4),(
32,1
2),o
r an
y (x
,y)
(6,1
) o
r (2
,4)
wh
ere
y �
4nan
d n
is a
p
osi
tive
od
d in
teg
er
7.5x
�14
y�
118.
7x�
3y�
40(5
,1),
(19,
6),o
r an
y (x
,y)
(4,4
) o
r (1
,11)
wh
ere
y �
5man
d m
is a
p
osi
tive
inte
ger
Enri
chm
ent
Cha
pter
218
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 2-3
Cha
pter
219
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 2
-3 i
n y
our
text
boo
k.
•W
hat
is
the
grad
e of
a r
oad
that
ris
es 4
0 fe
et o
ver
a h
oriz
onta
l di
stan
ce o
f 10
00 f
eet?
4%•
Wh
at i
s th
e gr
ade
of a
roa
d th
at r
ises
525
met
ers
over
a h
oriz
onta
l di
stan
ce o
f 10
kil
omet
ers?
(1
kilo
met
er �
1000
met
ers)
5.25
%
Rea
d t
he
Less
on
1.D
escr
ibe
each
typ
e of
slo
pe a
nd
incl
ude
a s
ketc
h.
Typ
e o
f S
lop
eD
escr
ipti
on
of
Gra
ph
Ske
tch
Pos
itive
Th
e lin
e ri
ses
to t
he
rig
ht.
Zer
oT
he
line
is h
ori
zon
tal.
Neg
ativ
eT
he
line
falls
to
th
e ri
gh
t.
Und
efin
edT
he
line
is v
erti
cal.
2.a.
How
are
th
e sl
opes
of
two
non
vert
ical
par
alle
l li
nes
rel
ated
?T
hey
are
eq
ual
.
b.
How
are
the
slo
pes
of t
wo
obli
que
perp
endi
cula
r li
nes
rela
ted?
Th
eir
pro
du
ct is
�1.
Rem
emb
er W
hat
Yo
u L
earn
ed
3.L
ook
up
the
term
s gr
ade,
pit
ch, s
lan
t, a
nd
slop
e. H
ow c
an e
very
day
mea
nin
gs o
f th
ese
wor
ds h
elp
you
rem
embe
r th
e de
fin
itio
n o
f sl
ope?
Sam
ple
an
swer
:All
thes
e w
ord
sca
n b
e u
sed
wh
en y
ou
des
crib
e h
ow m
uch
a t
hin
g s
lan
ts u
pw
ard
or
dow
nw
ard
.Yo
u c
an d
escr
ibe
this
nu
mer
ical
ly b
y co
mp
arin
g r
ise
to r
un
.
x
y
O
x
y
O
x
y
O
x
y
O
Less
on R
eadi
ng G
uide
Slo
pe
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A8
Chapter 2 A9 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-3)
Exer
cise
s
Cha
pter
220
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
Slo
pe
Slo
pe
mo
f a
Lin
eF
or p
oint
s (x
1, y
1) a
nd (
x 2,
y 2),
whe
re x
1�
x 2,
m�
�y 2
�y 1
� x 2�
x 1
chan
ge in
y�
�ch
ange
in x
Det
erm
ine
the
slop
e of
the
lin
e th
at p
asse
s th
rou
gh (
2, �
1) a
nd
(�4,
5).
m�
Slo
pe f
orm
ula
�(x
1, y
1) �
(2,
�1)
, (x
2, y
2) �
(�4,
5)
��
�1
Sim
plify
.
Th
e sl
ope
of t
he
lin
e is
�1.
6� �
6
5 �
(�1)
��
�4
�2
y 2�
y 1� x 2
�x 1
Gra
ph
th
e li
ne
pas
sin
gth
rou
gh (
�1,
�3)
wit
h a
slo
pe
of
.
Gra
ph t
he
orde
red
pair
(�
1, �
3). T
hen
,ac
cord
ing
to t
he
slop
e, g
o u
p 4
un
its
and
righ
t 5
un
its.
P
lot
the
new
poi
nt
(4,1
). C
onn
ect
the
poin
ts a
nd
draw
th
e li
ne.
x
y
O
4 � 5
Fin
d t
he
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.(4
, 7)
and
(6, 1
3)3
2.(6
, 4)
and
(3, 4
)0
3.(5
, 1)
and
(7, �
3)�
2
4.(5
, �3)
an
d (�
4, 3
)�
5.(5
, 10)
an
d (�
1,�
2)2
6.(�
1, �
4) a
nd (
�13
, 2)
�
7.(7
, �2)
an
d (3
, 3)
�8.
(�5,
9)
and
(5, 5
)�
9.(4
, �2)
an
d (�
4, �
8)
Gra
ph
th
e li
ne
pas
sin
g th
rou
gh t
he
give
n p
oin
t w
ith
th
e gi
ven
slo
pe.
10.s
lope
��
11.s
lope
�2
12.s
lope
�0
pass
es t
hro
ugh
(0,
2)
pass
es t
hro
ugh
(1,
4)
pass
es t
hro
ugh
(�
2, �
5)
13.s
lope
�1
14.s
lope
��
15.s
lope
�
pass
es t
hro
ugh
(�
4, 6
)pa
sses
th
rou
gh (
�3,
0)
pass
es t
hro
ugh
(0,
0)
1 � 53 � 4
x
y
O
x
y
Ox
y
O
1 � 3
3 � 42 � 5
5 � 4
1 � 2
2 � 3
Stud
y G
uide
and
Inte
rven
tion
Slo
pe
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exam
ple
1Ex
amp
le 2
Exer
cise
s
Exam
ple
2-3
Lesson 2-3
Para
llel a
nd
Per
pen
dic
ula
r Li
nes
Cha
pter
221
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
Stud
y G
uide
and
Inte
rven
tion
(co
ntin
ued)
Slo
pe
In a
pla
ne,
non
vert
ical
lin
es w
ith
th
esa
me
slop
e ar
e p
aral
lel.
All
ver
tica
lli
nes
are
par
alle
l.
x
y
O
slop
e �
m
slop
e �
m
In a
pla
ne,
tw
o ob
liqu
e li
nes
are
per
pen
dic
ula
rif
and
only
if
the
prod
uct
of
thei
r sl
opes
is
�1.
An
yve
rtic
al l
ine
is p
erpe
ndi
cula
r to
an
y h
oriz
onta
l li
ne.
x
y
O
slop
e �
m
slop
e �
�1 m
Are
th
e li
ne
pas
sin
g th
rou
gh (
2, 6
) an
d (
�2,
2)
and
th
e li
ne
pas
sin
gth
rou
gh (
3, 0
) an
d (
0, 4
) p
aral
lel,
per
pen
dic
ula
r, o
r n
eith
er?
Fin
d th
e sl
opes
of
the
two
lin
es.
Th
e sl
ope
of t
he
firs
t li
ne
is
�1.
Th
e sl
ope
of t
he
seco
nd
lin
e is
�
�.
Th
e sl
opes
are
not
equ
al a
nd
the
prod
uct
of
the
slop
es i
s n
ot �
1, s
o th
e li
nes
are
nei
ther
para
llel
nor
per
pen
dicu
lar.
Are
th
e li
nes
par
alle
l, p
erp
end
icu
lar,
or
nei
ther
?
1.th
e li
ne
pass
ing
thro
ugh
(4,
3)
and
(1, �
3) a
nd
the
lin
e pa
ssin
g th
rou
gh (
1, 2
) an
d (�
1,3)
per
pen
dic
ula
r
2.th
e li
ne
pass
ing
thro
ugh
(2,
8)
and
(�2,
2)
and
the
lin
e pa
ssin
g th
rou
gh (
0, 9
) an
d (6
, 0)
nei
ther
3.th
e li
ne
pass
ing
thro
ugh
(3,
9)
and
(�2,
�1)
an
d th
e gr
aph
of
y�
2xp
aral
lel
4.th
e li
ne
wit
h x
-in
terc
ept
�2
and
y-in
terc
ept
5 an
d th
e li
ne
wit
h x
-in
terc
ept
2 an
d y-
inte
rcep
t �
5p
aral
lel
5.th
e li
ne
wit
h x
-in
terc
ept
1 an
d y-
inte
rcep
t 3
and
the
lin
e w
ith
x-i
nte
rcep
t 3
and
y-in
terc
ept
1n
eith
er
6.th
e li
ne
pass
ing
thro
ugh
(�
2, �
3) a
nd
(2, 5
) an
d th
e gr
aph
of
x�
2y�
10p
erp
end
icu
lar
7.th
e li
ne
pass
ing
thro
ugh
(�
4, �
8) a
nd
(6, �
4) a
nd
the
grap
h o
f 2x
�5y
�5
par
alle
l
4 � 34
�0
� 0 �
3
6 �
2�
�2
�(�
2)
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A9
Chapter 2 A10 Glencoe Algebra 2
Answers (Lesson 2-3)
Cha
pter
222
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
Fin
d t
he
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.(1
, 5),
(�
1, �
3)4
2.(0
, 2),
(3,
0)
�3.
(1, 9
), (
0, 6
)3
4.(8
, �5)
, (4,
�2)
�5.
(�3,
5),
(�
3, �
1)u
nd
efin
ed6.
(�2,
�2)
, (10
, �2)
0
7.(4
, 5),
(2,
7)
�1
8.(�
2, �
4), (
3, 2
)9.
(5, 2
), (
�3,
2)
0
Gra
ph
th
e li
ne
pas
sin
g th
rou
gh t
he
give
n p
oin
t w
ith
th
e gi
ven
slo
pe.
10.(
0, 4
), m
�1
11.(
2, �
4), m
��
1
12.(
�3,
�5)
, m�
213
.(�
2, �
1), m
��
2
Gra
ph
th
e li
ne
that
sat
isfi
es e
ach
set
of
con
dit
ion
s.
14.p
asse
s th
rou
gh (
0, 1
), p
erpe
ndi
cula
r to
15.p
asse
s th
rou
gh (
0, �
5), p
aral
lel
to t
he
a li
ne
wh
ose
slop
e is
gr
aph
of
y�
1
16.H
IKIN
GN
aom
i le
ft f
rom
an
ele
vati
on o
f 74
00 f
eet
at 7
:00
A.M
.an
d h
iked
to
an e
leva
tion
of 9
800
feet
by
11:0
0 A.M
.Wh
at w
as h
er r
ate
of c
han
ge i
n a
ltit
ude
?60
0 ft
/h
(0 ,–
5)
x
y
O(0
,1)
x
y
O
1 � 3
(–2,
–1)
x
y
O
(–3,
–5)
x
y
O
( 2, –
4)x
y
O( 0
, 4)
x
y
O
6 � 5
3 � 4
2 � 3
Skill
s Pr
acti
ceS
lop
e
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 2-3
Cha
pter
223
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
Fin
d t
he
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.(3
, �8)
, (�
5, 2
)�
2.(�
10, �
3), (
7, 2
)3.
(�7,
�6)
, (3,
�6)
0
4.(8
, 2),
(8,
�1)
un
def
ined
5.(4
, 3),
(7,
�2)
�6.
(�6,
�3)
, (�
8, 4
)�
Gra
ph
th
e li
ne
pas
sin
g th
rou
gh t
he
give
n p
oin
t w
ith
th
e gi
ven
slo
pe.
7.(0
, �3)
, m�
38.
(2, 1
), m
��
9.(0
, 2),
m�
010
.(2,
�3)
, m�
Gra
ph
th
e li
ne
that
sat
isfi
es e
ach
set
of
con
dit
ion
s.
11.p
asse
s th
rou
gh (
3, 0
), p
erpe
ndi
cula
r12
.pas
ses
thro
ugh
(�
3, �
1), p
aral
lel
to a
lin
e
to a
lin
e w
hos
e sl
ope
is
wh
ose
slop
e is
�1
DEP
REC
IATI
ON
For
Exe
rcis
es 1
3–15
, use
th
e fo
llow
ing
info
rmat
ion
.A
mac
hin
e th
at o
rigi
nal
ly c
ost
$15,
600
has
a v
alu
e of
$75
00 a
t th
e en
d of
3 y
ears
. Th
e sa
me
mac
hin
e h
as a
val
ue
of $
2800
at
the
end
of 8
yea
rs.
13.F
ind
the
aver
age
rate
of
chan
ge i
n v
alu
e (d
epre
ciat
ion
) of
th
e m
ach
ine
betw
een
its
purc
has
e an
d th
e en
d of
3 y
ears
.�
$270
0 p
er y
ear
14.F
ind
the
aver
age
rate
of
chan
ge i
n v
alu
e of
th
e m
ach
ine
betw
een
th
e en
d of
3 y
ears
an
dth
e en
d of
8 y
ears
.�
$940
per
yea
r
15.I
nter
pret
the
sig
n of
you
r an
swer
s.It
is n
egat
ive
bec
ause
th
e va
lue
is d
ecre
asin
g.
( –3,
–1)
x
y
O
(3, 0
)x
y
O
3 � 2
( 2, –
3)
xO
y
( 0, 2
)
x
y
O
4 � 5
(2, 1
)
x
y
O
(0, –
3)
x
y
O
3 � 4
7 � 25 � 3
5 � 175 � 4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
S
lop
e
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A10
Chapter 2 A11 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-3)
1.TE
THER
Ate
ther
is
tied
tau
tly
to t
he
top
of a
pol
e as
sh
own
. Wh
at i
s th
e sl
ope
of t
he
teth
er?
2.A
VIA
TIO
NA
n a
irpl
ane
desc
ends
alo
ng
a st
raig
ht-
lin
e pa
th w
ith
a s
lope
of
�0.
1 to
lan
d at
an
air
port
. Use
th
ein
form
atio
n i
n t
he
diag
ram
to
dete
rmin
eth
e in
itia
l h
eigh
t of
th
e ai
rpla
ne.
5 m
iles
3.R
OC
K C
LIM
BIN
GT
he
tabl
e be
low
show
s G
ail’s
alt
itu
de a
bove
gro
un
ddu
rin
g a
rock
cli
mb
up
a cl
iff.
Com
plet
e th
e fo
llow
ing
tabl
e of
Gai
l’sav
erag
e ra
te o
f as
cen
t.
4.D
ESIG
NA
n a
rch
itec
t is
des
ign
ing
aw
indo
w w
ith
sla
nte
d in
teri
or b
ars.
Th
ecr
ossb
eam
is
perp
endi
cula
r to
th
e ot
her
fou
r ba
rs. W
hat
is
the
slop
e of
th
ecr
ossb
eam
?
�
REA
DIN
GF
or E
xerc
ises
5–7
, use
th
egr
aph
th
at s
how
s h
ow m
any
pag
es o
fh
er b
ook
Bri
dge
t re
ad e
ach
day
.
5.F
ind
the
aver
age
nu
mbe
r of
pag
esB
ridg
et r
ead
per
day.
20
6.O
n w
hic
h d
ays
did
Bri
dget
rea
d m
ore
page
s th
an h
er d
aily
ave
rage
?D
ay 2
an
d D
ay 3
7.If
Bri
dget
had
bee
n a
ble
to k
eep
up
the
pace
sh
e h
ad o
n d
ay 3
, how
man
y da
ysw
ould
it
hav
e ta
ken
her
to
fin
ish
th
ebo
ok?
5 d
aysPages Read
4060 20 080100
120
140
Day
32
15
47
6
1 � 3
4 ft
4 ft
4 ft
4 ft
12 ft
Cro
ss b
eam
50 m
iles
? m
iles
3 � 4
12 ft
9 ft
teth
er
Wor
d Pr
oble
m P
ract
ice
Slo
pe
Cha
pter
224
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Tim
eA
ltit
ud
e (m
)
10:0
00
10:2
022
10:4
030
11:0
033
Tim
e P
erio
dA
vera
ge
rate
of
asce
nt
(m/h
)
10:0
0-10
:20
6610
:20-
10:4
024
10:4
0-11
:00
9
Lesson 2-3
Th
e at
mos
pher
e is
com
pose
d of
abo
ut
50%
car
bon
dio
xide
, CO
2. T
he
leve
ls o
f ca
rbon
dio
xide
are
incr
easi
ng
due
to i
ncr
ease
fu
el c
onsu
mpt
ion
an
d h
ousi
ng
and
com
mer
cial
dev
elop
men
t.T
he
con
cen
trat
ion
of
a co
mpo
un
d is
mea
sure
d in
par
ts p
er m
illi
on (
ppm
). F
or e
xam
ple,
if
ther
e w
ere
500
CO
2m
olec
ule
s ou
t of
on
e m
illi
on a
ir p
arti
cles
, th
en t
he
CO
2le
vel
wou
ld b
e50
0 pp
m.
1.In
196
5, t
he
con
cen
trat
ion
of
CO
2w
as 3
20 p
pm. I
n 2
004,
th
e co
nce
ntr
atio
n w
as
378
ppm
. Det
erm
ine
the
rate
at
wh
ich
CO
2in
crea
sed
in p
pm p
er y
ear.
CO
2is
incr
ease
d a
pp
roxi
mat
ely
1.48
7 p
pm
per
yea
r.
2.C
arbo
n d
ioxi
de c
once
ntr
atio
n i
s re
late
d to
hu
man
con
sum
ptio
n o
f fo
ssil
fu
els
and
the
decr
ease
of
tree
s du
e to
dev
elop
men
t, t
her
efor
e an
in
crea
se i
n h
um
an p
opu
lati
on w
ill
resu
lt i
n a
n i
ncr
ease
in
car
bon
dio
xide
. In
198
0 th
e U
.S. p
opu
lati
on w
as 2
25 m
illi
on. T
he
2000
cen
sus
repo
rted
281
mil
lion
. At
wh
at r
ate
is t
he
popu
lati
on i
ncr
easi
ng
per
year
?W
hat
do
you
est
imat
e th
e U
.S. p
opu
lati
on t
o be
tod
ay?
U.S
.Po
pu
lati
on
is in
crea
sin
g a
bo
ut
2.8
mill
ion
peo
ple
per
yea
r.T
her
efo
re,
the
po
pu
lati
on
in 2
006
wo
uld
be
abo
ut
297.
8 m
illio
n.
3.U
se t
he
figu
res
from
Exe
rcis
es 1
an
d 2
to d
eter
min
e ab
out
how
mu
ch C
O2
is
“pro
duce
d” p
er m
illi
on p
eopl
e. I
s it
pos
sibl
e to
red
uce
th
e co
nce
ntr
atio
n o
f ca
rbon
dio
xide
in
th
e at
mos
pher
e w
hen
th
e h
um
an p
opu
lati
on i
s in
crea
sin
g?
Exp
lain
.0.
531
pp
m p
er m
illio
n p
eop
le;
Yes,
it is
po
ssib
le;
hu
man
s w
ou
ld h
ave
to r
edu
ce t
hei
r co
nsu
mp
tio
n o
ffo
ssil
fuel
s.
4.T
he
gree
nh
ouse
eff
ect
is h
eat
“tra
pped
” by
gas
es s
uch
as
carb
on d
ioxi
de, w
hic
h a
cts
as a
“bla
nke
t” f
or t
he
eart
h. H
igh
er c
once
ntr
atio
n l
evel
s of
car
bon
dio
xide
am
plif
y th
egr
een
hou
se e
ffec
t. T
hu
s, g
loba
l te
mpe
ratu
re i
s re
late
d to
th
e co
nce
ntr
atio
n o
f C
O2.
Rec
ords
in
dica
te t
hat
th
e in
crea
se i
n g
loba
l te
mpe
ratu
re s
ince
194
0 is
0.0
2 de
gree
sF
ahre
nh
eit
per
year
. Eac
h d
egre
e ri
se i
n t
empe
ratu
re c
ause
s oc
ean
lev
els
to r
ise
one-
hal
fa
foot
. Use
you
r da
ta t
o de
term
ine
in w
hat
yea
r th
e oc
ean
lev
el w
ill
rise
2 f
eet.
Wh
atim
pact
wil
l th
is h
ave
on c
oast
al r
egio
ns
of t
he
Un
ited
Sta
tes?
Cu
rren
t o
cean
leve
ls w
ill r
ise
2 fe
et in
200
yea
rs.
Th
is w
ou
ld d
ecre
ase
bea
ches
an
d p
oss
ibly
flo
od
so
me
coas
tal c
itie
s.
Cha
pter
225
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
Th
e In
crea
se in
Gre
enh
ou
se G
ases
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A11
Chapter 2 A12 Glencoe Algebra 2
Answers (Lesson 2-4)
Cha
pter
226
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 2
-4 i
n y
our
text
boo
k.
•If
th
e to
tal
cost
of
prod
uci
ng
a pr
odu
ct i
s gi
ven
by
the
equ
atio
n y
�54
00 �
1.37
x,
wh
at i
s th
e fi
xed
cost
? W
hat
is
the
vari
able
cos
t (f
or e
ach
ite
m p
rodu
ced)
?$5
400;
$1.3
7•
Wri
te a
lin
ear
equ
atio
n t
hat
des
crib
es t
he
foll
owin
g si
tuat
ion
:A
com
pan
y th
at m
anu
fact
ure
s co
mpu
ters
has
a f
ixed
cos
t of
$22
8,75
0 an
d a
vari
able
cos
tof
$85
2 to
pro
duce
eac
h c
ompu
ter.
y�
228,
750
�85
2x
Rea
d t
he
Less
on
1.a.
Wri
te t
he
slop
e-in
terc
ept
form
of
the
equ
atio
n o
f a
lin
e. T
hen
exp
lain
th
e m
ean
ing
ofea
ch o
f th
e va
riab
les
in t
he
equ
atio
n.
y�
mx
�b
;m
is t
he
slo
pe
and
bis
th
ey-
inte
rcep
t.T
he
vari
able
s x
and
yar
e th
e co
ord
inat
es o
f an
y p
oin
t o
nth
e lin
e.
b.
Wri
te t
he
poin
t-sl
ope
form
of
the
equ
atio
n o
f a
lin
e. T
hen
exp
lain
th
e m
ean
ing
of e
ach
of t
he
vari
able
s in
th
e eq
uat
ion
.y
�y 1
�m
(x�
x 1);
mis
th
e sl
op
e.x
and
yar
e th
e co
ord
inat
es o
f an
y p
oin
t o
n t
he
line.
x 1an
d y
1ar
e th
e co
ord
inat
es o
f o
ne
spec
ific
po
int
on
th
e lin
e.
2.S
upp
ose
that
you
r al
gebr
a te
ach
er a
sks
you
to
wri
te t
he
poin
t-sl
ope
form
of
the
equ
atio
nof
th
e li
ne
thro
ugh
th
e po
ints
(�
6, 7
) an
d (�
3, �
2). Y
ou w
rite
y�
2 �
�3(
x�
3) a
nd
you
r cl
assm
ate
wri
tes
y�
7 �
�3(
x�
6). W
hic
h o
f yo
u i
s co
rrec
t?E
xpla
in. Y
ou
are
bo
th c
orr
ect.
Eit
her
po
int
may
be
use
d a
s (x
1,y 1
) in
th
e p
oin
t-sl
op
e fo
rm.
You
use
d (
�3,
�2)
,an
d y
ou
r cl
assm
ate
use
d (
�6,
7).
3.Yo
u a
re a
sked
to
wri
te a
n e
quat
ion
of
two
lin
es t
hat
pas
s th
rou
gh (
3, �
5), o
ne
of t
hem
para
llel
to
and
one
of t
hem
per
pen
dicu
lar
to t
he
lin
e w
hos
e eq
uat
ion
is
y�
�3x
�4.
T
he
firs
t st
ep i
n f
indi
ng
thes
e eq
uat
ion
s is
to
fin
d th
eir
slop
es. W
hat
is
the
slop
e of
th
epa
rall
el l
ine?
Wh
at i
s th
e sl
ope
of t
he
perp
endi
cula
r li
ne?
�3;
Rem
emb
er W
hat
Yo
u L
earn
ed
4.M
any
stu
den
ts h
ave
trou
ble
rem
embe
rin
g th
e po
int-
slop
e fo
rm f
or a
lin
ear
equ
atio
n.
How
can
you
use
th
e de
fin
itio
n o
f sl
ope
to r
emem
ber
this
for
m?
Sam
ple
an
swer
:
Wri
te t
he
def
init
ion
of
slo
pe:
m�
.Mu
ltip
ly b
oth
sid
es o
f th
is
equ
atio
n b
y x 2
�x 1
.Dro
p t
he
sub
scri
pts
in y
2an
d x
2.T
his
giv
es t
he
po
int-
slo
pe
form
of
the
equ
atio
n o
f a
line.
y 2�
y 1� x 2
�x 1
1 � 3
Less
on R
eadi
ng G
uide
Wri
tin
g L
inea
r E
qu
atio
ns
Exer
cise
s
Exam
ple
2Ex
amp
le 1
Lesson 2-4
Form
s o
f Eq
uat
ion
s
Slo
pe-
Inte
rcep
t F
orm
o
f a
Lin
ear
Eq
uat
ion
y�
mx
�b,
whe
re m
is t
he s
lope
and
bis
the
y-in
terc
ept
Po
int-
Slo
pe
Fo
rm
y�
y 1�
m(x
�x 1
), w
here
(x 1
, y 1
) ar
e th
e co
ordi
nate
s of
a p
oint
on
the
line
and
of
a L
inea
r E
qu
atio
nm
is t
he s
lope
of
the
line
Stud
y G
uide
and
Inte
rven
tion
Wri
tin
g L
inea
r E
qu
atio
ns
Wri
te a
n e
qu
atio
n i
nsl
ope-
inte
rcep
t fo
rm f
or t
he
lin
e th
ath
as s
lop
e �
2 an
d p
asse
s th
rou
gh t
he
poi
nt
(3, 7
).
Su
bsti
tute
for
m, x
, an
d y
in t
he
slop
e-in
terc
ept
form
.y
�m
x�
bS
lope
-inte
rcep
t fo
rm
7 �
(�2)
(3)
�b
(x,
y)
�(3
, 7)
, m
��
2
7 �
�6
�b
Sim
plify
.
13 �
bA
dd 6
to
both
sid
es.
Th
e y-
inte
rcep
t is
13.
Th
e eq
uat
ion
in
sl
ope-
inte
rcep
t fo
rm i
s y
��
2x�
13.
Wri
te a
n e
qu
atio
n i
nsl
ope-
inte
rcep
t fo
rm f
or t
he
lin
e th
ath
as s
lop
e an
d x
-in
terc
ept
5.
y�
mx
�b
Slo
pe-in
terc
ept
form
0 �
��(5
) �
b(x
, y
) �
(5,
0),
m�
0 �
�b
Sim
plify
.
��
bS
ubtr
act
from
bot
h si
des.
Th
e y-
inte
rcep
t is
�. T
he
slop
e-in
terc
ept
form
is
y�
x�
.5 � 3
1 � 3
5 � 3
5 � 35 � 3
5 � 3
1 � 31 � 3
1 � 3
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
sat
isfi
es e
ach
set
of
con
dit
ion
s.
1.sl
ope
�2,
pas
ses
thro
ugh
(�
4, 6
)2.
slop
e , y
-in
terc
ept
4
y�
�2x
�2
y�
x�
4
3.sl
ope
1, p
asse
s th
rou
gh (
2, 5
)4.
slop
e �
, pas
ses
thro
ugh
(5,
�7)
y�
x�
3y
��
x�
6
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
eac
h g
rap
h.
5.6.
7.
y�
�3x
�9
y�
xy
�x
�1
4 � 91 � 9
5 � 4
x
y
O
( –4,
1)
( 5, 2
)
x
y O
( 4, 5
)
( 0, 0
)
x
y
O
( 1, 6
)
( 3, 0
)
13 � 513 � 5
3 � 23 � 2
Cha
pter
227
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A12
Chapter 2 A13 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-4)
Exer
cise
s
Exam
ple
1
Para
llel a
nd
Per
pen
dic
ula
r Li
nes
Use
th
e sl
ope-
inte
rcep
t or
poi
nt-
slop
e fo
rm t
o fi
nd
equ
atio
ns
of l
ines
th
at a
re p
aral
lel
or p
erpe
ndi
cula
r to
a g
iven
lin
e. R
emem
ber
that
par
alle
lli
nes
hav
e eq
ual
slo
pe. T
he
slop
es o
f tw
o pe
rpen
dicu
lar
lin
es a
re n
egat
ive
reci
proc
als,
th
atis
, th
eir
prod
uct
is
�1.
Stud
y G
uide
and
Inte
rven
tion
(co
ntin
ued)
Wri
tin
g L
inea
r E
qu
atio
ns
Wri
te a
n e
qu
atio
n o
f th
eli
ne
that
pas
ses
thro
ugh
(8,
2)
and
is
per
pen
dic
ula
r to
th
e li
ne
wh
ose
equ
atio
n i
s y
��
x�
3.
Th
e sl
ope
of t
he
give
n l
ine
is �
. Sin
ce t
he
slop
es o
f pe
rpen
dicu
lar
lin
es a
re n
egat
ive
reci
proc
als,
th
e sl
ope
of t
he
perp
endi
cula
rli
ne
is 2
.U
se t
he
slop
e an
d th
e gi
ven
poi
nt
to w
rite
the
equ
atio
n.
y�
y1
�m
(x�
x 1)
Poi
nt-s
lope
for
m
y�
2 �
2(x
�8)
(x1,
y1)
�(8
, 2)
, m
�2
y�
2 �
2x�
16D
istr
ibut
ive
Pro
p.
y�
2x�
14A
dd 2
to
each
sid
e.
An
equ
atio
n o
f th
e li
ne
is y
�2x
�14
.
1 � 2
1 � 2
Wri
te a
n e
qu
atio
n o
fth
e li
ne
that
pas
ses
thro
ugh
(�
1, 5
) an
dis
par
alle
l to
th
e gr
aph
of
y�
3x�
1.
Th
e sl
ope
of t
he
give
n l
ine
is 3
. Sin
ce t
he
slop
es o
f pa
rall
el l
ines
are
equ
al, t
he
slop
eof
th
e pa
rall
el l
ine
is a
lso
3.U
se t
he
slop
e an
d th
e gi
ven
poi
nt
to w
rite
the
equ
atio
n.
y�
y 1�
m(x
�x 1
)P
oint
-slo
pe f
orm
y�
5 �
3(x
�(�
1))
(x1,
y1)
�(�
1, 5
), m
�3
y�
5 �
3x�
3D
istr
ibut
ive
Pro
p.
y�
3x�
8A
dd 5
to
each
sid
e.
An
equ
atio
n o
f th
e li
ne
is y
�3x
�8.
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
sat
isfi
es e
ach
set
of
con
dit
ion
s.
1.pa
sses
th
rou
gh (
�4,
2),
par
alle
l to
th
e li
ne
wh
ose
equ
atio
n i
s y
�x
�5
y�
x�
4
2.pa
sses
th
rou
gh (
3, 1
), p
erpe
ndi
cula
r to
th
e gr
aph
of
y�
�3x
�2
y�
x
3.pa
sses
th
rou
gh (
1, �
1), p
aral
lel
to t
he
lin
e th
at p
asse
s th
rou
gh (
4, 1
) an
d (2
, �3)
y�
2x�
34.
pass
es t
hro
ugh
(4,
7),
per
pen
dicu
lar
to t
he
lin
e th
at p
asse
s th
rou
gh (
3, 6
) an
d (3
, 15)
y�
75.
pass
es t
hro
ugh
(8,
�6)
, per
pen
dicu
lar
to t
he
grap
h o
f 2x
�y
�4
y�
�x
�2
6.pa
sses
th
rou
gh (
2, �
2), p
erpe
ndi
cula
r to
th
e gr
aph
of
x�
5y�
6y
�5x
�12
7.pa
sses
th
rou
gh (
6, 1
), p
aral
lel
to t
he
lin
e w
ith
x-i
nte
rcep
t �
3 an
d y-
inte
rcep
t 5
y�
x�
98.
pass
es t
hro
ugh
(�
2, 1
), p
erpe
ndi
cula
r to
th
e li
ne
y�
4x�
11y
��
x�
1 � 21 � 4
5 � 3
1 � 2
1 � 3
1 � 21 � 2
Cha
pter
228
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exam
ple
2
Lesson 2-4
Sta
te t
he
slop
e an
d y
-in
terc
ept
of t
he
grap
h o
f ea
ch e
qu
atio
n.
1.y
�7x
�5
7,�
52.
y�
�x
�3
�,3
3.y
�x
,04.
3x�
4y�
4�
,1
5.7y
�4x
�7
,�1
6.3x
�2y
�6
�0
,3
7.2x
�y
�5
2,�
58.
2y�
6 �
5x�
,3
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
eac
h g
rap
h.
9.10
.11
.
y�
3x�
1y
��
1y
��
2x�
3
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
sat
isfi
es e
ach
set
of
con
dit
ion
s.
12.s
lope
3, p
asse
s th
rou
gh (
1, �
3)13
.slo
pe �
1, p
asse
s th
rou
gh (
0, 0
)
y�
3x�
6y
��
x
14.s
lope
�2,
pas
ses
thro
ugh
(0,
�5)
15.s
lope
3, p
asse
s th
rou
gh (
2, 0
)
y�
�2x
�5
y�
3x�
6
16.p
asse
s th
rou
gh (
�1,
�2)
an
d (�
3, 1
)17
.pas
ses
thro
ugh
(�
2, �
4) a
nd
(1, 8
)
y�
�x
�y
�4x
�4
18.x
-in
terc
ept
2, y
-in
terc
ept
�6
19.x
-in
terc
ept
, y-i
nte
rcep
t 5
y�
3x�
6y
��
2x�
5
20.p
asse
s th
rou
gh (
3, �
1), p
erpe
ndi
cula
r to
th
e gr
aph
of
y�
�x
�4.
y�
3x�
101 � 3
5 � 2
7 � 23 � 2
x
y
O
( 0, 3
)
( 3, –
3)
x
y
O( –
3, –
1)( 4
, –1)
x
y
O
( –1,
–4)
( 1, 2
)
5 � 2
3 � 24 � 7
3 � 42 � 3
2 � 3
3 � 53 � 5
Skill
s Pr
acti
ceW
riti
ng
Lin
ear
Eq
uat
ion
s
Cha
pter
229
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A13
Chapter 2 A14 Glencoe Algebra 2
Answers (Lesson 2-4)
Sta
te t
he
slop
e an
d y
-in
terc
ept
of t
he
grap
h o
f ea
ch e
qu
atio
n.
1.y
�8x
�12
8,12
2.y
�0.
25x
�1
0.25
,�1
3.y
��
x�
,0
4.3y
�7
0,5.
3x�
�15
�5y
,36.
2x�
3y�
10,�
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
eac
h g
rap
h.
7.8.
9.
y�
2y
�x
�2
y�
�x
�1
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
sat
isfi
es e
ach
set
of
con
dit
ion
s.
10.s
lope
�5,
pas
ses
thro
ugh
(�
3, �
8)11
.slo
pe
, pas
ses
thro
ugh
(10
, �3)
y�
�5x
�23
y�
x�
11
12.s
lope
0, p
asse
s th
rou
gh (
0, �
10)
13.s
lope
�, p
asse
s th
rou
gh (
6, �
8)
y�
�10
y�
�x
�4
14.p
asse
s th
rou
gh (
3, 1
1) a
nd
(�6,
5)
15.p
asse
s th
rou
gh (
7, �
2) a
nd
(3, �
1)
y�
x�
9y
��
x�
16.x
-in
terc
ept
3, y
-in
terc
ept
217
.x-i
nte
rcep
t �
5, y
-in
terc
ept
7
y�
�x
�2
y�
x�
7
18.p
asse
s th
rou
gh (
�8,
�7)
, per
pen
dicu
lar
to t
he
grap
h o
f y
�4x
�3
y�
�x
�9
19.R
ESER
VO
IRS
Th
e su
rfac
e of
Gra
nd
Lak
e is
at
an e
leva
tion
of
648
feet
. Du
rin
g th
ecu
rren
t dr
ough
t, t
he
wat
er l
evel
is
drop
pin
g at
a r
ate
of 3
in
ches
per
day
. If
this
tre
nd
con
tin
ues
, wri
te a
n e
quat
ion
th
at g
ives
th
e el
evat
ion
in
fee
t of
th
e su
rfac
e of
Gra
nd
Lak
eaf
ter
xda
ys.
y�
�0.
25x
�64
8
20.B
USI
NES
STo
ny
Mar
con
i’s c
ompa
ny
man
ufa
ctu
res
CD
-RO
M d
rive
s. T
he
com
pan
y w
ill
mak
e $1
50,0
00 p
rofi
t if
it
man
ufa
ctu
res
100,
000
driv
es, a
nd
$1,7
50,0
00 p
rofi
t if
it
man
ufa
ctu
res
500,
000
driv
es. T
he
rela
tion
ship
bet
wee
n t
he
nu
mbe
r of
dri
ves
man
ufa
ctu
red
and
the
prof
it i
s li
nea
r. W
rite
an
equ
atio
n t
hat
giv
es t
he
prof
it P
wh
en
ndr
ives
are
man
ufa
ctu
red.
P�
4n�
250,
000
1 � 4
7 � 52 � 3
1 � 41 � 4
2 � 3
2 � 32 � 3
4 � 54 � 5
2 � 33 � 2
x
y
O( 3
, –1)
( –3,
3)
x
y
O
( 4, 4
)
( 0, –
2)
x
y
O
( 0, 2
)
10 � 32 � 3
3 � 57 � 3
3 � 53 � 5
Prac
tice
W
riti
ng
Lin
ear
Eq
uat
ion
s
Cha
pter
230
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 2-4
Wor
d Pr
oble
m P
ract
ice
Wri
tin
g L
inea
r E
qu
atio
ns
Cha
pter
231
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.H
IKIN
GT
im b
egan
a h
ike
at t
he
base
of t
he
mou
nta
in t
hat
is
129
feet
abo
vese
a le
vel.
He
is h
ikin
g at
a s
tead
y ra
teof
5 f
eet
per
min
ute
. Let
Abe
his
alti
tude
abo
ve s
ea l
evel
in
fee
t an
d le
t t
be t
he
nu
mbe
r of
min
ute
s h
e h
as b
een
hik
ing.
Wri
te a
n e
quat
ion
in
slo
pe-
inte
rcep
t fo
rm t
hat
rep
rese
nts
how
man
y fe
et a
bove
sea
lev
el T
im h
ash
iked
. A
�5t
�12
9
2.C
HA
RIT
YB
y m
idn
igh
t, a
ch
arit
y h
adco
llec
ted
83 s
hir
ts. E
very
hou
r af
ter
that
, it
coll
ecte
d 20
mor
e sh
irts
. Let
hbe
the
nu
mbe
r of
hou
rs s
ince
mid
nig
ht
and
s be
th
e n
um
ber
of s
hir
ts. W
rite
a l
inea
req
uat
ion
in
slo
pe-i
nte
rcep
t fo
rm t
hat
rela
tes
the
nu
mbe
r of
sh
irts
col
lect
edan
d th
e n
um
ber
of h
ours
sin
ce m
idn
igh
t.s
�20
h�
83
3.M
APS
Th
e po
st o
ffic
e an
d ci
ty h
all
are
mar
ked
on a
coo
rdin
ate
plan
e. W
rite
th
eeq
uat
ion
of
the
lin
e in
slo
pe-i
nte
rcep
tfo
rm t
hat
pas
ses
thro
ugh
th
ese
two
poin
ts.
y�
x�
4.5
4.R
IGH
T TR
IAN
GLE
ST
he
lin
eco
nta
inin
g th
e ba
se o
f a
righ
t tr
ian
gle
has
th
e eq
uat
ion
y�
3x�
4. T
he
leg
perp
endi
cula
r to
th
e ba
se h
as a
nen
dpoi
nt
at (
6, 1
). W
hat
is
the
slop
e-in
terc
ept
form
of
the
equ
atio
n o
f th
e li
ne
con
tain
ing
the
leg?
y�
��1 3�
x�
3
DEC
OR
ATI
NG
For
Exe
rcis
es 5
–7, u
seth
e fo
llow
ing
info
rmat
ion
.
Agr
oup
of s
tude
nts
is
deco
rati
ng
a bu
llet
inbo
ard
that
mea
sure
s 3
feet
by
6 fe
et. T
hey
wan
t to
pu
t a
lin
e th
at s
tret
ches
fro
m t
he
upp
er r
igh
t co
rner
to
a po
int
2 fe
et u
p al
ong
the
left
edg
e as
sh
own
in
th
e fi
gure
.
5.U
sin
g th
e lo
wer
lef
t co
rner
of
the
bull
etin
boa
rd a
s th
e or
igin
, wh
at i
s th
eeq
uat
ion
of
the
lin
e in
slo
pe-i
nte
rcep
tfo
rm?
y�
x�
2
6.T
he
stu
den
ts c
han
ge t
hei
r m
ind
and
deci
de t
hat
th
e li
ne
shou
ld b
e lo
wer
edby
1 f
oot.
Wh
at i
s th
e eq
uat
ion
of
the
low
ered
lin
e in
slo
pe-i
nte
rcep
t fo
rm?
y�
x�
1
7.W
hat
are
th
e co
ordi
nat
es o
f th
e ce
nte
r of
the
bull
etin
boa
rd?
Doe
s th
e lo
wer
edli
ne
pass
th
rou
gh t
he
cen
ter?
Exp
lain
.(3
,1.5
);Ye
s,it
do
es b
ecau
se t
he
coo
rdin
ates
of
the
cen
ter
sati
sfy
the
equ
atio
n o
f th
e lo
wer
ed li
ne.
1 � 61 � 6
3 ft
2 ft
6 ft
3 � 2
y
xO
�3
�3
y
3
3
City
Hal
l
Post
Offic
e
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A14
Chapter 2 A15 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-4)
Two
-In
terc
ept
Fo
rm o
f a
Lin
ear
Eq
uat
ion
You
are
alre
ady
fam
ilia
r w
ith
the
slop
e-in
terc
ept
form
of
a li
near
equ
atio
n,
y�
mx
�b.
Lin
ear
equa
tion
s ca
n al
so b
e w
ritt
en i
n th
e fo
rm � ax �
�� by �
�1
wit
h
x-in
terc
ept
aan
d y-
inte
rcep
t b.
Thi
s is
cal
led
two-
inte
rcep
t fo
rm.
Dra
w t
he
grap
h o
f � �x 3�
�� 6y �
�1.
The
gra
ph c
ross
es t
he x
-axi
s at
�3
and
the
y-ax
is a
t 6.
Gra
ph
(�3,
0)
and
(0, 6
), th
en d
raw
a s
trai
ght
line
thr
ough
the
m.
Wri
te 3
x�
4y�
12 i
n t
wo-
inte
rcep
t fo
rm.
� 13 2x ��
� 14 2y ��
�1 12 2�D
ivid
e by
12
to o
btai
n 1
on t
he r
ight
sid
e.
� 4x ��
� 3y ��
1S
impl
ify.
Th
e x-
inte
rcep
t is
4; t
he
y-in
terc
ept
is 3
.
Use
th
e gi
ven
in
terc
epts
aan
d b
, to
wri
te a
n e
qu
atio
n i
n t
wo-
inte
rcep
t fo
rm. T
hen
dra
w t
he
grap
h.
See
stu
den
ts’g
rap
hs.
1.a
��
2, b
��
4� �x 2�
�� �y 4�
�1
2.a
�1,
b�
8�x 1�
��y 8�
�1
3.a
�3,
b�
5�x 3�
��y 5�
�1
4.a
�6,
b�
9�x 6�
��y 9�
�1
Wri
te e
ach
eq
uat
ion
in
tw
o-in
terc
ept
form
. Th
en d
raw
th
e gr
aph
.
5.3x
�2y
��
66.
�1 2� x�
�1 4� y�
17.
5x�
2y�
�10
� �x 2��
�y 3��
1�x 2�
��y 4�
�1
� �x 2��
� �y 5��
1
x
y
Ox
y
Ox
y
O
x
y O
Enri
chm
ent
Cha
pter
232
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exam
ple
1
Exam
ple
2
Exer
cise
s
Exer
cise
s
Exam
ple
Lesson 2-5
Cha
pter
233
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
Th
e sl
ope
inte
rcep
t fo
rm o
f a
lin
ear
equ
atio
n i
s y
�m
x�
b, w
her
e m
is t
he
slop
e an
d b
is t
he
y-in
terc
ept.
Rec
all
that
th
e fo
rmu
la f
or t
he
slop
e of
a l
ine
thro
ugh
(x 1
, y1)
an
d (x
2, y
2) i
s m
��y x2 2
� �y x1 1
�.Y
ou c
an u
se t
he
form
ula
for
slo
pe
and
the
slop
e-in
terc
ept
form
to
fin
d th
e va
lue
of b
.
Spre
adsh
eet
Act
ivit
yU
sin
g L
inea
r E
qu
atio
ns
Use
a s
pre
adsh
eet
to f
ind
th
e sl
ope
and
y-i
nte
rcep
t of
th
e li
ne
thro
ugh
eac
h p
air
ofp
oin
ts. T
hen
wri
te a
n e
qu
atio
n o
f th
e li
ne
in s
lop
e-in
terc
ept
form
.
1.(0
,�5)
, (2,
5)
2.(4
, 2),
(�
3, �
5)5,
�5;
y�
5x�
51,
�2;
y�
x�
2
3.(�
1, �
4), (
1, 3
)4.
(�4,
�9)
, (8,
3)
�7 2�,�
�1 2�;y
��7 2�x
��1 2�
1,�
5;y
�x
�5
5.(1
2, 9
), (
10, 1
0)6.
(�1.
5, 3
.1),
(0.
9, 1
.9)
��1 2�,
15;
y�
��1 2�x
�15
�0.
5,2.
35;
y�
�0.
5x�
2.35
7.D
oes
the
spre
adsh
eet
wor
k w
hen
tw
o po
ints
hav
e th
e sa
me
x-co
ordi
nat
es?
Exp
lain
.N
o;T
he
slo
pe
is u
nd
efin
ed.
Sta
te t
he
slop
e an
d y
-in
terc
ept
of t
he
grap
h o
f th
eli
ne
thro
ugh
(5,
2)
and
(4,
1).
Th
en w
rite
an
eq
uat
ion
of
the
lin
e in
slop
e-in
terc
ept
form
.
Ste
p1
Use
Col
um
ns
Aan
d B
to
repr
esen
t th
e fi
rst
poin
t, a
nd
Col
um
ns
Can
d D
to
repr
esen
t th
e se
con
d po
int
on t
he
lin
e. E
nte
r th
e fo
rmu
lafo
r sl
ope
in C
olu
mn
E.
Ste
p2
Su
bsti
tute
on
e of
th
e gi
ven
poi
nts
in
to t
he
slop
e-in
terc
ept
from
an
dso
lve
for
b. S
ince
we
know
th
e sl
ope
of t
he
lin
e, w
e ca
n s
olve
for
b.
y�
mx
�b
Slo
pe-in
terc
ept
form
y 1�
mx 1
�b
Sub
stitu
te (
x 1,
y 1).
y 1�
mx 1
�b
Sol
ve f
or b
.
En
ter
this
for
mu
la i
nto
Col
um
n F
usi
ng
the
nam
es o
f th
e sp
read
shee
t ce
lls.
Th
e sl
ope
of t
he
lin
e th
rou
gh (
5, 2
) an
d(4
, 1)
is 1
an
d th
e y-
inte
rcep
t is
�3.
Th
us,
th
e eq
uat
ion
of
the
lin
e sl
ope-
inte
rcep
t fo
rm i
s y
�1x
�(�
3) o
r y
�x
�3.
1 2 3
A x 15
B y 12
C x 24
D y 21
ES
lope 1
Fy-
inte
rcep
t�
3
Sh
eet
1S
hee
t 2
Sh
eet
3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A15
Chapter 2 A16 Glencoe Algebra 2
Answers (Lesson 2-5)
Cha
pter
234
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
Less
on R
eadi
ng G
uide
Mo
del
ing
Rea
l-W
orl
d D
ata:
Usi
ng
Sca
tter
Plo
tsG
et R
ead
y fo
r th
e Le
sso
nR
ead
th
e in
trod
uct
ion
to
Les
son
2-5
in
you
r te
xtb
ook
.
•If
a w
oman
ru
ns
5.5
mil
es p
er h
our,
abo
ut
how
man
y C
alor
ies
wil
l sh
e bu
rn i
n a
n h
our?
Sam
ple
an
swer
:57
2 C
alo
ries
•If
a m
an r
un
s 7.
5 m
iles
per
hou
r, a
bou
t h
ow m
any
Cal
orie
s w
ill
he
burn
in
hal
f an
hou
r?S
amp
le a
nsw
er:
397
Cal
ori
es
Rea
d t
he
Less
on
1.S
upp
ose
that
a s
et o
f da
ta c
an b
e m
odel
ed b
y a
lin
ear
equ
atio
n. E
xpla
in t
he
diff
eren
cebe
twee
n a
sca
tter
plo
t of
th
e da
ta a
nd
a gr
aph
of
the
lin
ear
equ
atio
n t
hat
mod
els
that
data
.S
amp
le a
nsw
er:T
he
scat
ter
plo
t is
a d
iscr
ete
gra
ph
.It
is m
ade
up
just
of
the
ind
ivid
ual
po
ints
th
at r
epre
sen
t th
e d
ata
po
ints
.Th
e lin
ear
equ
atio
nh
as a
co
nti
nu
ou
s g
rap
h t
hat
is t
he
line
that
bes
t fi
ts t
he
dat
a p
oin
ts.
2.S
upp
ose
that
tu
itio
n a
t a
stat
e co
lleg
e w
as $
3800
per
yea
r in
200
0 an
d h
as b
een
incr
easi
ng
at a
rat
e of
$20
0 pe
r ye
ar.
a.W
rite
a p
redi
ctio
n e
quat
ion
th
at e
xpre
sses
th
is i
nfo
rmat
ion
.y
�38
00 �
200x
b.
Exp
lain
th
e m
ean
ing
of e
ach
var
iabl
e in
you
r pr
edic
tion
equ
atio
n.
xre
pre
sen
ts t
he
nu
mb
er o
f ye
ars
sin
ce 2
000
and
yre
pre
sen
ts t
he
tuit
ion
in t
hat
yea
r.
3.U
se t
his
mod
el t
o pr
edic
t th
e tu
itio
n a
t th
is c
olle
ge i
n 2
007.
$520
0
Rem
emb
er W
hat
Yo
u L
earn
ed
4.L
ook
up
the
wor
d sc
atte
rin
a d
icti
onar
y. H
ow c
an i
ts d
efin
itio
n h
elp
you
to
rem
embe
rth
e m
ean
ing
of t
he
diff
eren
ce b
etw
een
a s
catt
er p
lot
and
the
grap
h o
f a
lin
ear
equ
atio
n?
Sam
ple
an
swer
:To
sca
tter
mea
ns
to b
reak
up
an
d g
o in
man
y d
irec
tio
ns.
Th
e p
oin
ts o
n a
sca
tter
plo
t ar
e b
roke
n u
p.I
n t
he
gra
ph
of
a lin
ear
equ
atio
n,t
he
po
ints
are
co
nn
ecte
d t
o f
orm
a c
on
tin
uo
us
line.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exer
cise
s
Exam
ple
Lesson 2-5
Scat
ter
Plo
tsW
hen
a s
et o
f da
ta p
oin
ts i
s gr
aph
ed a
s or
dere
d pa
irs
in a
coo
rdin
ate
plan
e, t
he
grap
h i
s ca
lled
a s
catt
er p
lot.
Asc
atte
r pl
ot c
an b
e u
sed
to d
eter
min
e if
th
ere
isa
rela
tion
ship
am
ong
the
data
.
BA
SEB
ALL
Th
e ta
ble
bel
ow s
how
s th
e n
um
ber
of
hom
e ru
ns
and
run
s b
atte
d i
n f
or v
ario
us
bas
ebal
l p
laye
rs w
ho
hav
e w
on t
he
Mos
t V
alu
able
Pla
yer
Aw
ard
sin
ce 2
002.
Mak
e a
scat
ter
plo
t of
th
e d
ata.
Sour
ce:w
ww.b
aseb
all-re
fere
nce.c
om
Mak
e a
scat
ter
plo
t fo
r th
e d
ata
in e
ach
tab
le b
elow
.
1.FU
EL E
FFIC
IEN
CY
Th
e ta
ble
belo
w s
how
s th
e av
erag
e fu
el e
ffic
ien
cy i
n m
iles
per
gal
lon
of
veh
icle
s in
th
e U
.S.
duri
ng
the
year
s li
sted
.
Sour
ce:U
.S. F
eder
al Hi
ghwa
y Ad
min
istra
tion
2.C
ON
GR
ESS
Th
e ta
ble
belo
w s
how
s th
e n
um
ber
of
wom
en w
ho
serv
ed i
n t
he
Un
ited
Sta
tes
Con
gres
s du
rin
g th
e ye
ars
1995
�20
06.
Sour
ce:w
ww.se
nate
.gov
Co
ng
ress
ion
al S
essi
on
Nu
mb
er o
f Wo
men
104
59
105
65
106
67
107
75
108
77
109
83
Wo
men
in
Co
ng
ress
Number of Women
5560 06570758085
Sess
ion
of
Co
ng
ress
104
106
108
110
Year
Fu
el E
ffic
ien
cy (
mp
g)
1970
12.0
1980
13.3
1990
16.4
2000
16.9
Avera
ge F
uel
Eff
icie
ncy
Miles per Gallon
36912151821
1970
1980
1990
2000
0
MV
P H
Rs
an
d R
BIs
Runs Batted In
5075 25 0
100
125
150
Ho
me
Ru
ns
1812
630
4224
3648
Ho
me
Ru
ns
Ru
ns
Bat
ted
In
4611
0
3413
1
4590
4711
8
4510
1
3912
6
Cha
pter
235
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
Stud
y G
uide
and
Inte
rven
tion
Mo
del
ing
Rea
l-W
orl
d D
ata:
Usi
ng
Sca
tter
Plo
ts
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A16
Chapter 2 A17 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-5)
Exam
ple
Pred
icti
on
Eq
uat
ion
sA
lin
e of
fit
is a
lin
e th
at c
lose
ly a
ppro
xim
ates
a s
et o
f da
tagr
aph
ed i
n a
sca
tter
plo
t. T
he
equ
atio
n o
f a
lin
e of
fit
is
call
ed a
pre
dic
tion
eq
uat
ion
beca
use
it
can
be
use
d to
pre
dict
val
ues
not
giv
en i
n t
he
data
set
.
To f
ind
a pr
edic
tion
equ
atio
n f
or a
set
of
data
, sel
ect
two
poin
ts t
hat
see
m t
o re
pres
ent
the
data
wel
l. T
hen
to
wri
te t
he
pred
icti
on e
quat
ion
, use
wh
at y
ou k
now
abo
ut
wri
tin
g a
lin
ear
equ
atio
n w
hen
giv
en t
wo
poin
ts o
n t
he
lin
e.
STO
RA
GE
CO
STS
Acc
ord
ing
to a
cer
tain
pre
dic
tion
eq
uat
ion
, th
eco
st o
f 20
0 sq
uar
e fe
et o
f st
orag
e sp
ace
is $
60. T
he
cost
of
325
squ
are
feet
of
stor
age
spac
e is
$16
0.
a.F
ind
th
e sl
ope
of t
he
pre
dic
tion
eq
uat
ion
. Wh
at d
oes
it r
epre
sen
t?S
ince
th
e co
st d
epen
ds u
pon
th
e sq
uar
e fo
otag
e, l
et x
repr
esen
t th
e am
oun
t of
sto
rage
spac
e in
squ
are
feet
an
d y
repr
esen
t th
e co
st i
n d
olla
rs. T
he
slop
e ca
n b
e fo
un
d u
sin
g th
e
form
ula
m�
. So,
m�
��
0.8
Th
e sl
ope
of t
he
pred
icti
on e
quat
ion
is
0.8.
Th
is m
ean
s th
at t
he
pric
e of
sto
rage
in
crea
ses
80¢
for
each
on
e-sq
uar
e-fo
ot i
ncr
ease
in
sto
rage
spa
ce.
b.
Fin
d a
pre
dic
tion
eq
uat
ion
.U
sin
g th
e sl
ope
and
one
of t
he
poin
ts o
n t
he
lin
e, y
ou c
an u
se t
he
poin
t-sl
ope
form
to
fin
da
pred
icti
on e
quat
ion
.
y�
y 1�
m(x
�x 1
)P
oint
-slo
pe f
orm
y�
60 �
0.8(
x�
200)
(x1,
y1)
�(2
00,
60),
m�
0.8
y�
60 �
0.8x
�16
0D
istr
ibut
ive
Pro
pert
y
y�
0.8x
�10
0A
dd 6
0 to
bot
h si
des.
Apr
edic
tion
equ
atio
n i
s y
�0.
8x�
100.
SALA
RIE
ST
he
tab
le b
elow
sh
ows
the
year
s of
exp
erie
nce
for
eig
ht
tech
nic
ian
s at
Lew
is T
ech
omat
ic a
nd
th
e h
ourl
y ra
te o
f p
ay e
ach
tec
hn
icia
n e
arn
s. U
se t
he
dat
afo
r E
xerc
ises
1 a
nd
2.
Exp
erie
nce
(ye
ars)
94
31
106
128
Ho
url
y R
ate
of
Pay
$17
$10
$10
$7$1
9$1
2$2
0$1
5
1.D
raw
a s
catt
er p
lot
to s
how
how
yea
rs o
f ex
peri
ence
are
re
late
d to
hou
rly
rate
of
pay.
Dra
w a
lin
e of
fit
.S
ee g
rap
h.
2.W
rite
a p
redi
ctio
n e
quat
ion
to
show
how
yea
rs o
f ex
peri
ence
(x)
are
rela
ted
to h
ourl
y ra
te o
f pa
y (y
).S
amp
le a
nsw
eru
sin
g (
1,7)
an
d (
9,17
):y
�1.
25x
�5.
75
Exp
erie
nce
(ye
ars)
Hourly Pay ($)
20
610
48
1214
24 20 16 12 8 4
Tech
nic
ian
Sala
ries
100
� 125
160
�60
��
325
�20
0y 2
�y 1
� x 2�
x 1
Cha
pter
236
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
Stud
y G
uide
and
Inte
rven
tion
(co
ntin
ued)
Mo
del
ing
Rea
l-W
orl
d D
ata:
Usi
ng
Sca
tter
Plo
ts
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exer
cise
s
Skill
s Pr
acti
ceM
od
elin
g R
eal-
Wo
rld
Dat
a:U
sin
g S
catt
er P
lots
Lesson 2-5
For
Exe
rcis
es 1
–3, c
omp
lete
par
ts a
–c f
or e
ach
set
of
dat
a.
a.D
raw
a s
catt
er p
lot.
b.
Use
tw
o or
der
ed p
airs
to
wri
te a
pre
dic
tion
eq
uat
ion
.c.
Use
you
r p
red
icti
on e
qu
atio
n t
o p
red
ict
the
mis
sin
g va
lue.
1.1a
.
1b.
Sam
ple
an
swer
usi
ng
(1,
1) a
nd
(8,
15):
y�
2x�
11c
.S
amp
le a
nsw
er:
19
2.2a
.
2b.
Sam
ple
an
swer
usi
ng
(5,
9) a
nd
(40
,44)
:y
�x
�4
2c.
Sam
ple
an
swer
:54
3.3a
.
3b.
Sam
ple
an
swer
usi
ng
(2,
16)
and
(7,
34):
y�
3.6x
�8.
83c
.S
amp
le a
nsw
er:
19.6
13
57
24
68
36 30 24 18 12 6 0x
yx
y
116
216
3?
422
530
734
836
515
2535
1020
3040
40 32 24 16 8 0x
yx
y
59
1017
2022
2530
3538
4044
50?
13
57
24
68
15 12 9 6 3 0x
yx
y
11
35
47
611
712
815
10?
Cha
pter
237
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A17
Chapter 2 A18 Glencoe Algebra 2
Answers (Lesson 2-5)
Prac
tice
M
od
elin
g R
eal-
Wo
rld
Dat
a:U
sin
g S
catt
er P
lots
For
Exe
rcis
es 1
–3, c
omp
lete
par
ts a
–c f
or e
ach
set
of
dat
a.a.
Dra
w a
sca
tter
plo
t.b
.U
se t
wo
ord
ered
pai
rs t
o w
rite
a p
red
icti
on e
qu
atio
n.
c.U
se y
our
pre
dic
tion
eq
uat
ion
to
pre
dic
t th
e m
issi
ng
valu
e.
1.FU
EL E
CO
NO
MY
Th
e ta
ble
give
s th
e ap
prox
imat
e w
eigh
ts i
n t
ons
and
esti
mat
es
for
over
all
fuel
eco
nom
y in
mil
es p
er g
allo
n
for
seve
ral
cars
.1b
.Sam
ple
an
swer
usi
ng
(1.
4,24
) an
d
(2.4
,15)
:y
��
9x�
36.6
1c.S
amp
le a
nsw
er:
18.6
mi/g
al
2.A
LTIT
UD
EIn
mos
t ca
ses,
tem
pera
ture
dec
reas
es w
ith
in
crea
sin
g al
titu
de. A
s A
nch
ara
driv
es i
nto
th
e m
oun
tain
s, h
er c
ar t
her
mom
eter
reg
iste
rs t
he
tem
pera
ture
s (°
F)
show
nin
th
e ta
ble
at t
he
give
n a
ltit
ude
s (f
eet)
.
2b.S
amp
le a
nsw
er u
sin
g (
7500
,61)
an
d
(970
0,50
):y
��
0.00
5x�
98.5
2c.S
amp
le a
nsw
er:
38.5
°F
3.H
EALT
HA
lton
has
a t
read
mil
l th
at u
ses
the
tim
e on
th
e tr
eadm
ill
and
the
spee
d of
w
alki
ng
or r
un
nin
g to
est
imat
e th
e n
um
ber
of C
alor
ies
he
burn
s du
rin
g a
wor
kou
t. T
he
tabl
e gi
ves
wor
kou
t ti
mes
an
d C
alor
ies
burn
ed f
or s
ever
al w
orko
uts
.
3b.S
amp
le a
nsw
er u
sin
g (
24,2
80)
and
(48,
440)
:y
�6.
67x
�11
9.92
3c.S
amp
le a
nsw
er:
abo
ut
520
Cal
ori
es
Tim
e (m
in)
Calories Burned
010
2030
4050
555
1525
3545
500
400
300
200
100
Bu
rnin
g C
alo
ries
Tim
e (m
in)
1824
3040
4248
5260
Cal
ori
es B
urn
ed26
028
032
038
040
044
047
5?
Alt
itu
de
(ft)
Temperature (�F)
07,
000
8,00
09,
000
10,0
00
65 60 55 50 45
Tem
pera
ture
Vers
us
Alt
itu
de
Alt
itu
de
(ft)
7500
8200
8600
9200
9700
10,4
0012
,000
Tem
per
atu
re (
�F)
6158
5653
5046
?
Wei
gh
t (t
on
s)
Fuel Economy (mi/gal)
00.
51.
01.
52.
02.
5
30 25 20 15 10 5Fuel
Eco
no
my V
ers
us
Weig
ht
Wei
gh
t (t
on
s)1.
31.
41.
51.
82
2.1
2.4
Mile
s p
er G
allo
n29
2423
21?
1715
Cha
pter
238
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Mo
del
ing
Rea
l-W
orl
d D
ata:
Usi
ng
Sca
tter
Plo
ts
Lesson 2-5
Cha
pter
239
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.A
IRC
RA
FTT
he
tabl
e sh
ows
the
max
imu
m s
peed
an
d al
titu
de o
f di
ffer
ent
airc
raft
. Dra
w a
sca
tter
plo
t of
th
is d
ata.
Sour
ce:w
ww.ri
singu
p.co
m
2.TE
STIN
GT
he
scat
ter
plot
sh
ows
the
hei
ght
and
test
sco
res
of s
tude
nts
in
am
ath
cla
ss. D
escr
ibe
the
corr
elat
ion
betw
een
hei
ghts
an
d te
st s
core
s.
Th
ere
is n
o c
orr
elat
ion
.3.
STO
CK
ST
he
pric
es o
f a
tech
nol
ogy
stoc
k ov
er 5
day
s ar
e sh
own
in
th
e ta
ble.
Dra
w a
sca
tter
plo
t of
th
e da
ta a
nd
ali
ne
of f
it.
4.A
LGA
ET
he
scat
ter
plot
sh
ows
data
reco
rdin
g th
e am
oun
t of
alg
ae a
nd
the
tem
pera
ture
of
the
wat
er i
n v
ario
us
aqu
ariu
m t
anks
. Dra
w a
lin
e of
fit
for
this
dat
a an
d w
rite
a p
redi
ctio
neq
uat
ion
.
Sam
ple
an
swer
:y
�4x
�6
SPO
RTS
For
Exe
rcis
es 5
an
d 6
, use
th
esc
atte
r p
lot
show
ing
the
hei
ght
and
scor
e of
dif
fere
nt
con
test
ants
sh
ooti
ng
dar
ts.
5.W
hat
is
the
equ
atio
n o
f th
e li
ne
of f
it?
Sam
ple
ans
wer
:y�
0.3x
�2
6.W
hat
do
you
pre
dict
som
eon
e 5
feet
tal
lw
ould
sco
re?
10 p
oin
tsScore1012 68 24 0H
eig
ht
(ft)5
63
41
2
Temperature (°C)
25
Alg
ae (
po
un
ds)
56
43
21
0510152030
Stock Price
8.30
8.45
8.15 0
8.60
8.75
8.90
9.05
8.20
9.35
Day
12
34
5
Day
12
34
5
BT
EK
8.30
8.60
8.55
8.90
9.30
Test Score
5060708090 40100
Hei
gh
t (i
n.)
062
6466
6870
72
Maximum Altitude(thousands of ft)
1416 12 0182022
Max
imu
m S
pee
d (
kno
ts)
140
120
160
180
Max
.Sp
eed
(k
no
ts)
121
123
137
173
153
Max
.Alt
itu
de
(100
0 fe
et)
14.2
17.0
15.3
20.7
16.0
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A18
Chapter 2 A19 Glencoe Algebra 2
An
swer
s
Answers (Lessons 2-5 and 2-6)
Enri
chm
ent
Med
ian
-Fit
Lin
es
Am
edia
n-f
it li
ne
is a
par
ticu
lar
type
of
lin
e of
fit
. Fol
low
th
e st
eps
belo
w t
o fi
nd
the
equ
atio
n o
f th
e m
edia
n-f
it l
ine
for
the
data
.
Ap
pro
xim
ate
Per
cen
tag
e o
f Vio
len
t C
rim
es C
om
mit
ted
by
Juve
nile
s T
hat
Vic
tim
s R
epo
rted
to
Law
En
forc
emen
t
Year
1980
1982
1984
1986
1988
1990
1992
1994
1996
Off
end
ers
3635
3332
3130
2929
30
Sour
ce: U
.S. B
urea
u of
Justi
ce S
tatis
tics
1.D
ivid
e th
e da
ta i
nto
th
ree
appr
oxim
atel
y eq
ual
gro
ups
. Th
ere
shou
ld a
lway
s be
th
e sa
me
nu
mbe
r of
poi
nts
in
th
e fi
rst
and
thir
d gr
oups
. In
th
is c
ase,
th
ere
wil
l be
th
ree
data
poi
nts
in
eac
h g
rou
p.
Gro
up
1G
rou
p 2
Gro
up
3Ye
arO
ffen
der
sYe
arO
ffen
der
sYe
arO
ffen
der
s19
8036
1986
3219
9229
1982
3519
8831
1994
2919
8433
1990
3019
9630
2.F
ind
x 1, x
2, a
nd
x 3, t
he
med
ian
s of
th
e x
valu
es i
n g
rou
ps 1
, 2, a
nd
3,
resp
ecti
vely
. Fin
d y 1
, y2,
an
d y 3
, th
e m
edia
ns
of t
he
yva
lues
in
gro
ups
1,
2, a
nd
3, r
espe
ctiv
ely.
1982
,198
8,19
94;
35,3
1,29
3.F
ind
an e
quat
ion
of
the
lin
e th
rou
gh (
x 1, y
1) a
nd
(x3,
y3)
.y
��
0.5x
�10
26
4.F
ind
Y, t
he
y-co
ordi
nat
e of
th
e po
int
on t
he
lin
e in
Exe
rcis
e 2
wit
h a
n
x-co
ordi
nat
e of
x2.
32
5.T
he
med
ian
-fit
lin
e is
par
alle
l to
th
e li
ne
in E
xerc
ise
2, b
ut
is o
ne-
thir
d
clos
er t
o (x
2, y
2). T
his
mea
ns
it p
asse
s th
rou
gh �x
2, �2 3� Y
��1 3�
y 2�. F
ind
this
or
dere
d pa
ir. a
bo
ut
(198
8,31
.67)
6.W
rite
an
equ
atio
n o
f th
e m
edia
n-f
it l
ine.
y�
�0.
5x�
1025
.67
7.U
se t
he
med
ian
-fit
lin
e to
pre
dict
th
e pe
rcen
tage
of
juve
nil
e vi
olen
t cr
ime
offe
nde
rs i
n 2
010
and
2020
.20
10:
abo
ut
21%
;20
20:
abo
ut
16%
Cha
pter
240
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 2-6
Cha
pter
241
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Sp
ecia
l Fu
nct
ion
sG
et R
ead
y fo
r th
e Le
sso
nR
ead
th
e in
trod
uct
ion
to
Les
son
2-6
in
you
r te
xtb
ook
.
•W
hat
is
the
cost
of
mai
lin
g a
lett
er t
hat
wei
ghs
0.5
oun
ce?
$0.3
7 o
r 37
cen
ts•
Giv
e th
ree
diff
eren
t w
eigh
ts o
f le
tter
s th
at w
ould
eac
h c
ost
60 c
ents
to
mai
l.A
nsw
ers
will
var
y.S
amp
le a
nsw
er:
1.1
ou
nce
s,1.
9 o
un
ces,
2.0
ou
nce
s
Rea
d t
he
Less
on
1.F
ind
the
valu
e of
eac
h e
xpre
ssio
n.
a.⏐�
3⏐�
��3�
�
b.
⏐6.2
⏐�
�6.2
��
c.⏐�
4.01
⏐�
��4.
01�
�
2.Te
ll h
ow t
he
nam
e of
eac
h k
ind
of f
un
ctio
n c
an h
elp
you
rem
embe
r w
hat
th
e gr
aph
lo
oks
like
.
a.co
nst
ant
fun
ctio
nS
amp
le a
nsw
er:
So
met
hin
g is
co
nst
ant
if it
do
es n
ot
chan
ge.
Th
e y-
valu
es o
f a
con
stan
t fu
nct
ion
do
no
t ch
ang
e,so
th
eg
rap
h is
a h
ori
zon
tal l
ine.
b.
abso
lute
val
ue
fun
ctio
nS
amp
le a
nsw
er:T
he
abso
lute
val
ue
of
a n
um
ber
tells
yo
u h
ow
far
it is
fro
m 0
on
th
e n
um
ber
lin
e.It
mak
es n
o d
iffe
ren
cew
het
her
yo
u g
o t
o t
he
left
or
rig
ht
so lo
ng
as
you
go
th
e sa
me
dis
tan
ce e
ach
tim
e.
c.st
ep f
un
ctio
nS
amp
le a
nsw
er:
A s
tep
fu
nct
ion
’s g
rap
h lo
oks
like
ste
ps
that
go
up
or
do
wn
.
d.
iden
tity
fu
nct
ion
Sam
ple
an
swer
:Th
e x-
an
d y
-val
ues
are
alw
ays
iden
tica
lly t
he
sam
e fo
r an
y p
oin
t o
n t
he
gra
ph
.So
th
e g
rap
h is
a li
ne
thro
ug
h t
he
ori
gin
th
at h
as s
lop
e 1.
Rem
emb
er W
hat
Yo
u L
earn
ed
3.M
any
stu
den
ts f
ind
the
grea
test
in
tege
r fu
nct
ion
con
fusi
ng.
Exp
lain
how
you
can
use
an
um
ber
lin
e to
fin
d th
e va
lue
of t
his
fu
nct
ion
for
an
y re
al n
um
ber.
An
swer
s w
illva
ry.S
amp
le a
nsw
er:
Dra
w a
nu
mb
er li
ne
that
sh
ow
s th
e in
teg
ers.
To f
ind
the
valu
e o
f th
e g
reat
est
inte
ger
fu
nct
ion
fo
r an
y re
al n
um
ber
,pla
ce t
hat
nu
mb
er o
n t
he
nu
mb
er li
ne.
If it
is a
n in
teg
er,t
he
valu
e o
f th
e fu
nct
ion
isth
e n
um
ber
itse
lf.I
f n
ot,
mov
e to
th
e in
teg
er d
irec
tly
to t
he
left
of
the
nu
mb
er y
ou
ch
ose
.Th
is in
teg
er w
ill g
ive
the
valu
e yo
u n
eed
.
�5
4.01
66.
2
�3
3
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A19
Chapter 2 A20 Glencoe Algebra 2
Answers (Lesson 2-6)
Cha
pter
242
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
Stud
y G
uide
and
Inte
rven
tion
Sp
ecia
l Fu
nct
ion
sSt
ep F
un
ctio
ns,
Co
nst
ant
Fun
ctio
ns,
an
d t
he
Iden
tity
Fu
nct
ion
Th
e ch
art
belo
w l
ists
som
e sp
ecia
l fu
nct
ion
s yo
u s
hou
ld b
e fa
mil
iar
wit
h.
Fu
nct
ion
Wri
tten
as
Gra
ph
Con
stan
tf(
x) �
cho
rizon
tal l
ine
Iden
tity
f(x)
�x
line
thro
ugh
the
orig
in w
ith s
lope
1
Gre
ates
t In
tege
r F
unct
ion
f(x)
��x
�on
e-un
it ho
rizon
tal s
egm
ents
, w
ith r
ight
end
poin
ts m
issi
ng,
arra
nged
lik
e st
eps
Th
e gr
eate
st i
nte
ger
fun
ctio
n i
s an
exa
mpl
e of
a s
tep
fu
nct
ion
, a f
un
ctio
n w
ith
a g
raph
th
atco
nsi
sts
of h
oriz
onta
l se
gmen
ts.
Iden
tify
eac
h f
un
ctio
n a
s a
con
stan
t fu
nct
ion
, th
e id
enti
tyfu
nct
ion
, or
a st
ep f
un
ctio
n.
a.b
.
a co
nst
ant
fun
ctio
na
step
fu
nct
ion
Iden
tify
eac
h f
un
ctio
n a
s a
con
stan
t fu
nct
ion
, th
e id
enti
ty f
un
ctio
n, a
gre
ates
tin
tege
r fu
nct
ion
, or
a st
ep f
un
ctio
n.
1.2.
3.
a co
nst
ant
fun
ctio
na
step
fu
nct
ion
the
iden
tity
fu
nct
ionx
f (x)
Ox
f (x)
Ox
f (x)
O
x
f (x)
Ox
f (x)
O
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exam
ple
Exer
cise
s
Lesson 2-6
Cha
pter
243
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(co
ntin
ued)
Sp
ecia
l Fu
nct
ion
sA
bso
lute
Val
ue
and
Pie
cew
ise
Fun
ctio
ns
Fu
nct
ion
Wri
tten
as
Gra
ph
Ab
solu
te V
alu
e F
un
ctio
nf(
x)
�⏐x
⏐tw
o ra
ys th
at a
re m
irror
imag
es o
f eac
h ot
her
and
mee
t at a
poi
nt, t
he v
erte
x
Th
e ab
solu
te v
alu
e fu
nct
ion
can
be
wri
tten
as
a p
iece
wis
e fu
nct
ion
. Api
ecew
ise
fun
ctio
nis
wri
tten
usi
ng
two
or m
ore
expr
essi
ons.
Its
gra
ph i
s of
ten
dis
join
ted.
Gra
ph
f(x
) �
3⏐x⏐
�4.
Fin
d se
vera
l or
dere
d pa
irs.
Gra
ph t
he
poin
ts a
nd
con
nec
t th
em. Y
ou w
ould
exp
ect
the
grap
h t
o lo
oksi
mil
ar t
o it
s pa
ren
t fu
nct
ion
, f(x
) �
⏐x⏐.
Gra
ph
f(x
) �
�2xif
x�
2x
�1
if x
�2.
Fir
st, g
raph
th
e li
nea
r fu
nct
ion
f(x
) �
2xfo
r x
�2.
Sin
ce 2
doe
s n
otsa
tisf
y th
is i
neq
ual
ity,
sto
p w
ith
a c
ircl
e at
(2,
4).
Nex
t, g
raph
th
eli
nea
r fu
nct
ion
f(x
) �
x�
1 fo
r x
�2.
Sin
ce 2
doe
s sa
tisf
y th
isin
equ
alit
y, b
egin
wit
h a
dot
at
(2, 1
).
Gra
ph
eac
h f
un
ctio
n. I
den
tify
th
e d
omai
n a
nd
ran
ge.
1.g(
x) �
��2.
h(x
) �
⏐2x
�1⏐
3.h
(x)
�
do
mai
n:
all r
eal
do
mai
n:
all r
eal
do
mai
n:
all r
eal
nu
mb
ers;
ran
ge:
nu
mb
ers;
ran
ge:
nu
mb
ers;
ran
ge:
all i
nte
ger
s{y
⏐y�
0}{y
⏐y
1}
x
y
O
x
y
O
x
y
Ox � 3
x
f (x)
O
x
f (x)
O
x3⏐
x⏐�
4
0�
4
1�
1
22
�1
�1
�2
2
⎧ ⎪ ⎨ ⎪ ⎩
if x
0
2x�
6 if
0 �
x�
21
if x
�2
x � 3
Exam
ple
1
Exam
ple
2
Exer
cise
s
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A20
Chapter 2 A21 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-6)
Cha
pter
244
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
Skill
s Pr
acti
ceS
pec
ial F
un
ctio
ns
Iden
tify
eac
h f
un
ctio
n a
s S
for
ste
p, C
for
con
stan
t, A
for
abso
lute
val
ue,
or
Pfo
rp
iece
wis
e.
1.2.
3.
SC
A
Gra
ph
eac
h f
un
ctio
n. I
den
tify
th
e d
omai
n a
nd
ran
ge.
4.f(
x) �
�x�
1�5.
f(x)
��x
�3�
D �
all r
eals
,R �
all i
nte
ger
sD
�al
l rea
ls,R
�al
l in
teg
ers
6.g(
x) �
2⏐x⏐
7.f(
x) �
⏐x⏐
�1
D �
all r
eals
,D
�al
l rea
ls,R
�{y
⏐⏐ y�
1}R
�n
on
neg
ativ
e re
als
8.f(
x) �
�xif
x�
09.
h(x
) �
�3 if
x�
�1
2 if
x�
0x
�1
if x
> 1
D �
all r
eals
,D
�{x
⏐x�
�1
or
x
1},
R �
{y⏐y
�0
or
y�
2}R
�{y
⏐y
2}
x
h (x)
O
x
f (x)
O
x
f (x)
Ox
g(x)
O
x
f (x)
O
x
f (x)
O
x
y
O
x
y
Ox
y
O
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 2-6
Cha
pter
245
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Gra
ph
eac
h f
un
ctio
n. I
den
tify
th
e d
omai
n a
nd
ran
ge.
1.f(
x) �
�0.5
x�2.
f(x)
��x
��
2
D �
all r
eals
,R �
all i
nte
ger
sD
�al
l rea
ls,R
�al
l in
teg
ers
3.g(
x) �
�2⏐
x⏐4.
f(x)
�⏐x
�1⏐
D �
all r
eals
,D
�al
l rea
ls,
R �
no
np
osi
tive
rea
ls
R �
no
nn
egat
ive
real
s
5.f(
x) �
�x�
2 if
x
�2
6.h
(x)
��4
�x
if x
0
3xif
x
�2
�2x
�2
if x
�0
D �
all r
eals
,R �
all r
eals
D �
all n
on
zero
rea
ls,R
�al
l rea
ls7.
BU
SIN
ESS
AS
titc
h i
n T
ime
char
ges
8.
BU
SIN
ESS
Aw
hol
esal
er c
har
ges
a st
ore
$3.0
0
$40
per
hou
r or
an
y fr
acti
on t
her
eof
per
poun
d fo
r le
ss t
han
20 p
ound
s of
can
dy a
ndfo
r la
bor.
Dra
w a
gra
ph o
f th
e st
ep
$2.5
0 pe
r po
un
d fo
r 20
or
mor
e po
un
ds. D
raw
afu
nct
ion
th
at r
epre
sen
ts t
his
sit
uat
ion
.gr
aph
of
the
fun
ctio
n t
hat
rep
rese
nts
th
issi
tuat
ion
.
Ho
urs
Total Cost ($)
10
35
24
67
280
240
200
160
120 80 40
Lab
or
Co
sts
Pou
nd
s
Cost ($)
50
1525
1020
3035
105 90 75 60 45 30 15
Can
dy C
ost
s
x
h (x)
O
f(x)
xO
x
f (x)
O
x
g (x)
O
x
f (x)
Ox
f (x)
OPrac
tice
S
pec
ial F
un
ctio
ns
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A21
Chapter 2 A22 Glencoe Algebra 2
Answers (Lesson 2-6)
Cha
pter
246
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.SA
VIN
GS
Nat
han
pu
ts $
200
into
ach
ecki
ng
acco
un
t as
soo
n a
s h
e ge
ts h
ispa
ych
eck.
Th
e va
lue
of h
is c
hec
kin
gac
cou
nt
is m
odel
ed b
y th
e fo
rmu
la20
0�m
�, w
her
e m
is t
he
nu
mbe
r of
mon
ths
that
Nat
han
has
bee
n w
orki
ng.
Aft
er 1
05 d
ays,
how
mu
ch m
oney
is
inth
e ac
cou
nt?
$600
2.FI
NA
NC
EA
fin
anci
al a
dvis
or h
andl
esth
e tr
ansa
ctio
ns
in a
ban
k ac
cou
nt.
For
ever
y tr
ansa
ctio
n, t
he
advi
sor
gets
a 5
%co
mm
issi
on, r
egar
dles
s of
wh
eth
er t
he
tran
sact
ion
is
a de
posi
t or
wit
hdr
awal
.W
rite
a f
orm
ula
usi
ng
the
abso
lute
valu
e fu
nct
ion
for
th
e ad
viso
r’s
com
mis
sion
. Let
Dre
pres
ent
the
valu
eof
on
e tr
ansa
ctio
n.
C�
0.05
⏐⏐D⏐⏐
or
C�
⏐⏐0.0
5D⏐⏐
3.R
OU
ND
ING
Asc
ien
ce t
each
er i
nst
ruct
sst
ude
nts
to
rou
nd
thei
r m
easu
rem
ents
as f
ollo
ws:
If
a n
um
ber
is l
ess
than
0.5
of a
mil
lim
eter
, stu
den
ts a
re i
nst
ruct
edto
rou
nd
dow
n. I
f a
nu
mbe
r is
exa
ctly
0.5
or g
reat
er, s
tude
nts
are
tol
d to
rou
nd
up
to t
he
nex
t m
illi
met
er. W
rite
afo
rmu
la t
hat
tak
es a
mea
sure
men
t x
and
yiel
ds t
he
rou
nde
d of
f n
um
ber.
I��x
�.0
5�m
m
4.A
RC
HIT
ECTU
RE
Th
e cr
oss-
sect
ion
of
aro
of i
s sh
own
in
th
e fi
gure
. Wri
te a
nab
solu
te v
alu
e fu
nct
ion
th
at m
odel
s th
esh
ape
of t
he
roof
.
y�
6�
⏐⏐x�
3 ⏐⏐
GA
MES
For
Exe
rcis
es 5
an
d 6
, use
th
efo
llow
ing
info
rmat
ion
.
Som
e yo
un
g pe
ople
are
pla
yin
g a
gam
ew
her
e a
woo
den
pla
nk
is u
sed
as a
tar
get.
It
is
mar
ked
off
into
6 e
qual
par
ts. A
valu
eis
wri
tten
in
eac
h s
ecti
on t
o re
pres
ent
the
scor
e ea
rned
if
the
dart
lan
ds i
n t
hat
sect
ion
. Let
xde
not
e th
e h
oriz
onta
l po
siti
onof
a d
art
on t
he
boar
d, w
her
e th
e ce
nte
r of
the
boar
d is
th
e or
igin
. Neg
ativ
e va
lues
corr
espo
nd
to t
he
left
hal
f of
th
e da
rt b
oard
,an
d po
siti
ve v
alu
es c
orre
spon
d to
th
e ri
ght
hal
f. A
play
er’s
sco
re d
epen
ds o
n t
he
dist
ance
of
the
dart
fro
m t
he
orig
in.
5.W
rite
a f
orm
ula
th
at g
ives
th
eh
oriz
onta
l di
stan
ce f
rom
th
e ce
nte
r of
the
dart
boar
d.d
�⏐⏐ x
⏐⏐
6.W
rite
a f
orm
ula
usi
ng
the
grea
test
inte
ger
fun
ctio
n t
hat
can
be
use
d to
fin
dth
e pe
rson
’s s
core
.S
�3
�� ⏐⏐
x ⏐⏐�y
xO
Wor
d Pr
oble
m P
ract
ice
Sp
ecia
l Fu
nct
ion
s
Lesson 2-6
Cha
pter
247
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Gra
ph
ing
Gre
ates
t In
teg
er F
un
ctio
ns
Som
e eq
uat
ion
s in
volv
ing
the
grea
test
in
tege
r fu
nct
ion
pro
duce
in
tere
stin
g gr
aph
s.
It w
ill
be h
elpf
ul
to m
ake
a ch
art
of v
alu
es f
or e
ach
fu
nct
ion
an
d to
use
a c
olor
ed
pen
or
pen
cil.
Gra
ph
eac
h f
un
ctio
n.
1.y
�2x
��x
�2.
y�
�� �x x� ��
3.y
��� �0 0. .5 5x x
� �
1 1� ��
4.y
�� �x x��
x
y
O1
–1–2
–3–4
23
4
4 3 2 1 –1 –2 –3 –4
x
y
O1
–1–2
–3–4
23
4
4 3 2 1 –1 –2 –3 –4
x
y
O1
–1–2
–3–4
23
4
4 3 2 1 –1 –2 –3 –4
x
y
O1
–1–2
–3–4
23
4
4 3 2 1 –1 –2 –3 –4
Enri
chm
ent
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A22
Chapter 2 A23 Glencoe Algebra 2
An
swer
s
Answers (Lessons 2-6 and 2-7)
Exam
ple
Cha
pter
248
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Gra
phin
g Ca
lcul
ator
Act
ivit
yTr
ansf
orm
atio
ns:
Gre
ates
t In
teg
er F
un
ctio
n
Agr
aph
ing
calc
ula
tor
can
be
use
d to
dis
play
tra
nsf
orm
atio
ns
to t
he
grea
test
inte
ger
fun
ctio
n. T
his
is
don
e by
usi
ng
the
int(
com
man
d u
nde
r th
e M
AT
H:
NU
Mm
enu
. Wh
en g
raph
ing
the
grea
test
in
tege
r fu
nct
ion
, it
is i
mpo
rtan
t to
set
the
calc
ula
tor
to D
ot m
ode.
Gra
ph
eac
h f
un
ctio
n. E
valu
ate
it f
or x
�1,
x�
1.3,
an
d x
�2.
Com
par
e th
e gr
aph
of
the
fun
ctio
n t
o th
e gr
aph
of
f(x)
�[[x
]].
1.g(
x)�
[[x]]
�3
2.g(
x) �
[[x�
2]]
3.g(
x) �
[[x+
4]]
[�4.
7, 4
.7] s
cl: 1
by
[�3.
1, 3
.1] s
cl: 1
[�4.
7, 4
.7] s
cl: 1
by
[�3.
1, 3
.1] s
cl: 1
[�4.
7, 4
.7] s
cl: 1
by
[�3.
1, 3
.1] s
cl: 1
g(1
)��
2,g
(1.3
) ��
2,g
(2) �
�1
g(1
) ��
1,g
(1.3
) ��
1,g
(2) �
0g
(1) �
5,g
(1.3
) �5,
g(2
) �6
shift
ed d
own
3 un
itssh
ifted
rig
ht 2
uni
tssh
ifted
left
4 un
its
4.g(
x) �
[[�x]
]5.
g(x)
�[[2
x]]
6.g(
x) �
3[[x
]]
[�4.
7, 4
.7] s
cl: 1
by
[�3.
1, 3
.1] s
cl: 1
[�4.
7, 4
.7] s
cl: 1
by
[�3.
1, 3
.1] s
cl: 1
[�4.
7, 4
.7] s
cl: 1
by
[�3.
1, 3
.1] s
cl: 1
g(1
)��
1,g
(1.3
) ��
2,g
(2) �
�2
g(1
) �2,
g(1
.3) �
2,g
(2) �
4g
(1)�
3,g
(1.3
)�3,
g(2
)�6
refle
cted
acr
oss
the
y-ax
isco
mpr
esse
d by
�1 2�ho
rizo
ntal
lyex
pand
ed b
y 3
vert
ical
ly
Gra
ph
f(x
)�
[[x]]
and
g(x
) �
[[x]]
�2
on t
he
sam
e ax
es.
Eva
luat
e ea
ch f
un
ctio
n f
or x
�0.
6, x
�1,
x�
1.3,
x�
2, x
��
0.5,
an
dx
��
1.1.
Com
par
e th
e gr
aph
s of
th
e fu
nct
ion
s.E
nte
r f(
x) i
n Y
1an
d g(
x) i
n Y
2. G
raph
th
e fu
nct
ion
s.K
eyst
roke
s:
5 5
2 6
4.
Use
TR
AC
Eto
eva
luat
e ea
ch f
un
ctio
n f
or t
he
give
n v
alu
es.
Key
stro
kes:
0.
6 1
1.3
2 0.
5
1.1
0.6
1 1.
3 2
0.5
1.1
.
f(0.
6)�
0, f(
1) �
1, f(
1.3)
�1,
f(2)
�2,
f(�
0.5)
��
1, a
nd f(
�1.
1) �
�2
g(0.
6) �
2, g
(1) �
3, g
(1.3
) �3,
g(2
) �4,
g(�
0.5)
��
1, a
nd g
(�1.
1) �
0
Th
e gr
aph
of
g(x)
�[[x
�2]
]is
th
e sa
me
as t
he
grap
h o
f f(
x)�
[[x]]
shif
ted
2 u
nit
s u
p.
EN
TER
(–)
EN
TER
(–)
EN
TER
EN
TER
EN
TER
EN
TER
EN
TER
(–)
EN
TER
(–)
EN
TER
EN
TER
EN
TER
EN
TER
TR
AC
E
ZO
OM
ZO
OM
EN
TER
+)
MA
TH
EN
TER
)M
AT
HY
=
[�4.
7, 4
.7] s
cl:1
by
[�3.
1, 3
.1] s
cl:1
Exer
cise
s
Lesson 2-7
Cha
pter
249
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 2
-7 i
n y
our
text
boo
k.
•W
hic
h o
f th
e co
mbi
nat
ion
s of
pas
sin
g ya
rds
and
tou
chdo
wn
pas
ses
list
ed w
ould
Dan
aco
nsi
der
a go
od g
ame?
Th
e fi
rst
on
e:16
8 ya
rds
and
3 t
ou
chd
ow
ns
•S
upp
ose
that
in
on
e of
th
e ga
mes
Dan
a pl
ays,
Ble
dsoe
pas
ses
157
yard
s. W
hat
is
the
smal
lest
nu
mbe
r of
tou
chdo
wn
pas
ses
he
mu
st g
et i
n o
rder
for
Dan
a to
con
side
r th
is a
good
gam
e?3
Rea
d t
he
Less
on
1.W
hen
gra
phin
g a
lin
ear
ineq
ual
ity
in t
wo
vari
able
s, h
ow d
o yo
u k
now
wh
eth
er t
o m
ake
the
bou
nda
ry a
sol
id l
ine
or a
das
hed
lin
e? If
th
e sy
mb
ol i
s �
or
,t
he
line
isso
lid.
If t
he
sym
bo
l is
o
r �
,th
e lin
e is
das
hed
.
2.H
ow d
o yo
u k
now
wh
ich
sid
e of
th
e bo
un
dary
to
shad
e?S
amp
le a
nsw
er:
If t
he
test
po
int
giv
es a
tru
e in
equ
alit
y,sh
ade
the
reg
ion
co
nta
inin
g t
he
test
po
int.
Ifth
e te
st p
oin
t g
ives
a f
alse
ineq
ual
ity,
shad
e th
e re
gio
n n
ot
con
tain
ing
the
test
po
int.
3.M
atch
eac
h i
neq
ual
ity
wit
h i
ts g
raph
.
a.y
2x
�3
iiib
.y
��
2x�
3iv
c.y
�2x
�3
iid
.y
��
2x�
3i
i. ii
. ii
i. iv
.
Rem
emb
er W
hat
Yo
u L
earn
ed
4.D
escr
ibe
som
e w
ays
in w
hic
h g
raph
ing
an i
neq
ual
ity
in o
ne
vari
able
on
a n
um
ber
lin
e is
sim
ilar
to
grap
hin
g an
in
equ
alit
y in
tw
o va
riab
les
in a
coo
rdin
ate
plan
e. H
ow c
an w
hat
you
kn
ow a
bou
t gr
aph
ing
ineq
ual
itie
s on
a n
um
ber
lin
e h
elp
you
to
grap
h i
neq
ual
itie
s in
a co
ordi
nat
e pl
ane?
Sam
ple
an
swer
:A
bo
un
dar
y o
n a
co
ord
inat
e g
rap
h is
sim
ilar
to a
n e
nd
po
int
on
a n
um
ber
lin
e g
rap
h.A
das
hed
lin
e is
sim
ilar
toa
circ
le o
n a
nu
mb
er li
ne:
bo
th a
re o
pen
an
d m
ean
no
t in
clu
ded
;th
eyre
pre
sen
t th
e sy
mb
ols
an
d �
.A s
olid
lin
e is
sim
ilar
to a
do
t o
n a
nu
mb
er li
ne:
bo
th a
re c
lose
d a
nd
mea
n in
clu
ded
;th
ey r
epre
sen
t th
esy
mb
ols
�an
d
.
x
y
O
x
y
Ox
y
O
x
y
OLess
on R
eadi
ng G
uide
Gra
ph
ing
Ineq
ual
itie
s
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A23
Chapter 2 A24 Glencoe Algebra 2
Answers (Lesson 2-7)
Cha
pter
250
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
Gra
ph
Lin
ear
Ineq
ual
itie
sA
lin
ear
ineq
ual
ity,
lik
e y
�2x
�1,
res
embl
es a
lin
ear
equ
atio
n, b
ut
wit
h a
n i
neq
ual
ity
sign
in
stea
d of
an
equ
als
sign
. Th
e gr
aph
of
the
rela
ted
lin
ear
equ
atio
n s
epar
ates
th
e co
ordi
nat
e pl
ane
into
tw
o h
alf-
plan
es. T
he
lin
e is
th
ebo
un
dary
of
each
hal
f-pl
ane.
To g
raph
a l
inea
r in
equ
alit
y, f
ollo
w t
hes
e st
eps.
1.G
raph
th
e bo
un
dary
; th
at i
s, t
he
rela
ted
lin
ear
equ
atio
n. I
f th
e in
equ
alit
y sy
mbo
l is
or �
, th
e bo
un
dary
is
soli
d. I
f th
e in
equ
alit
y sy
mbo
l is
�or
, t
he
bou
nda
ry i
s da
shed
.2.
Ch
oose
a p
oin
t n
ot o
n t
he
bou
nda
ry a
nd
test
it
in t
he
ineq
ual
ity.
(0,
0)
is a
goo
d po
int
toch
oose
if
the
bou
nda
ry d
oes
not
pas
s th
rou
gh t
he
orig
in.
3.If
a t
rue
ineq
ual
ity
resu
lts,
sh
ade
the
hal
f-pl
ane
con
tain
ing
you
r te
st p
oin
t. I
f a
fals
ein
equ
alit
y re
sult
s, s
had
e th
e ot
her
hal
f-pl
ane.
Gra
ph
x�
2y�
4.
Th
e bo
un
dary
is
the
grap
h o
f x
�2y
�4.
Use
th
e sl
ope-
inte
rcep
t fo
rm, y
��
x�
2, t
o gr
aph
th
e bo
un
dary
lin
e.
Th
e bo
un
dary
lin
e sh
ould
be
soli
d.
Now
tes
t th
e po
int
(0, 0
).
0 �
2(0)
�?
4(x
, y
) �
(0,
0)
0 �
4fa
lse
Sh
ade
the
regi
on t
hat
doe
s n
otco
nta
in (
0, 0
).
Gra
ph
eac
h i
neq
ual
ity.
1.y
�3x
�1
2.y
�x
�5
3.4x
�y
�
1
4.y
��
45.
x�
y
66.
0.5x
�0.
25y
�1.
5
x
y
O
x
y
O
x
y
O
x � 2
x
y
O
x
y
O
x
y
O
1 � 2x
y O
Stud
y G
uide
and
Inte
rven
tion
Gra
ph
ing
Ineq
ual
itie
s
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exam
ple
Exer
cise
s
Lesson 2-7
Cha
pter
251
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
Gra
ph
Ab
solu
te V
alu
e In
equ
alit
ies
Gra
phin
g ab
solu
te v
alu
e in
equ
alit
ies
is s
imil
arto
gra
phin
g li
nea
r in
equ
alit
ies.
Th
e gr
aph
of
the
rela
ted
abso
lute
val
ue
equ
atio
n i
s th
ebo
un
dary
. Th
is b
oun
dary
is
grap
hed
as
a so
lid
lin
e if
th
e in
equ
alit
y is
or
�, a
nd
dash
ed i
fth
e in
equ
alit
y is
�or
. C
hoo
se a
tes
t po
int
not
on
th
e bo
un
dary
to
dete
rmin
e w
hic
h r
egio
nto
sh
ade.
Gra
ph
y
3⏐x
�1⏐
.
Fir
st g
raph
th
e eq
uat
ion
y�
3⏐x
�1⏐
.S
ince
th
e in
equ
alit
y is
, t
he
grap
h o
f th
e bo
un
dary
is
soli
d.Te
st (
0, 0
).0
?3⏐
0 �
1⏐(x
, y)
�(0
, 0)
0 ?
3⏐�
1⏐⏐�
1⏐�
1
0
3tr
ue
Sh
ade
the
regi
on t
hat
con
tain
s (0
, 0).
Gra
ph
eac
h i
neq
ual
ity.
1.y
�⏐x
⏐�
12.
y
⏐2x
�1⏐
3.y
�2⏐
x⏐
3
4.y
��
⏐x⏐
�3
5.⏐x
⏐�
y�
46.
⏐x�
1⏐�
2y�
0
7.⏐2
�x⏐
�y
�
18.
y�
3⏐x⏐
�3
9.y
⏐1
�x⏐
�4 x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
Ox
y
Ox
y
O
x
y
O
Stud
y G
uide
and
Inte
rven
tion
(co
ntin
ued)
Gra
ph
ing
Ineq
ual
itie
s
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exam
ple
Exer
cise
s
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A24
Chapter 2 A25 Glencoe Algebra 2
An
swer
s
Answers (Lesson 2-7)
Gra
ph
eac
h i
neq
ual
ity.
1.y
1
2.y
x
�2
3.x
�y
4
4.x
�3
�y
5.2
�y
�x
6.y
��
x
7.x
�y
�
28.
9x�
3y�
6
09.
y�
1 �
2x
10.y
�7
�
911
.x
�5
12.y
⏐x
⏐
x
y
Ox
y
Ox
y
O
x
y
Ox
y
Ox
y
O
x
y
Ox
y
O
x
y
O
x
y
O
x
y
Ox
y
O
Cha
pter
252
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
Skill
s Pr
acti
ceG
rap
hin
g In
equ
alit
ies
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2-7
Lesson 2-7
Cha
pter
253
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Gra
ph
eac
h i
neq
ual
ity.
1.y
�
32.
x
23.
x�
y
�4
4.y
��
3x�
55.
y�
x�
36.
y�
1 �
�x
7.x
�3y
6
8.y
⏐x
⏐�
19.
y
�3⏐
x�
1⏐�
2
CO
MPU
TER
SF
or E
xerc
ises
10–
12, u
se t
he
foll
owin
g in
form
atio
n.
Asc
hoo
l sy
stem
is
buyi
ng
new
com
pute
rs. T
hey
wil
l bu
y de
skto
p co
mpu
ters
cos
tin
g $1
000
per
un
it, a
nd
not
eboo
k co
mpu
ters
cos
tin
g $1
200
per
un
it. T
he
tota
l co
st o
f th
e co
mpu
ters
can
not
exc
eed
$80,
000.
10.W
rite
an
in
equ
alit
y th
at d
escr
ibes
th
is s
itu
atio
n.
1000
d�
1200
n
80,0
00
11.G
raph
th
e in
equ
alit
y.
12.I
f th
e sc
hoo
l w
ants
to
buy
50 o
f th
e de
skto
p co
mpu
ters
an
d 25
of
the
not
eboo
k co
mpu
ters
, w
ill
they
hav
e en
ough
mon
ey?
yes
Des
kto
ps
Notebooks
100
3050
2040
6070
8090
100
80 70 60 50 40 30 20 10
Co
mp
ute
rs P
urc
hase
d
x
y
O
x
y
Ox
y O
x
y
Ox
y
O
x
y
O
1 � 2
x
y
O
x
y
O
x
y
O
Prac
tice
Gra
ph
ing
Ineq
ual
itie
s
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A25
Chapter 2 A26 Glencoe Algebra 2
Answers (Lesson 2-7)
Cha
pter
254
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.FR
AM
EST
he
dim
ensi
ons
of a
rect
angu
lar
fram
e th
at c
an b
e m
ade
from
a 5
0 in
ch p
lan
k of
woo
d ar
e li
mit
edby
th
e in
equ
alit
y �
�w
25
. Gra
phth
is i
neq
ual
ity.
2.B
UIL
DIN
G C
OD
EA
city
has
a b
uil
din
gco
de t
hat
lim
its
the
hei
ght
of b
uil
din
gsar
oun
d th
e ce
ntr
al p
ark.
Th
e co
de s
ays
that
all
bu
ildi
ngs
mu
st b
e le
ss t
han
0.1
xin
hei
ght
wh
ere
xis
th
e di
stan
ce o
f th
ebu
ildi
ng
from
th
e ce
nte
r of
th
e pa
rk.
Ass
um
e th
at t
he
park
cen
ter
is l
ocat
edat
0. G
raph
th
e in
equ
alit
y th
atre
pres
ents
th
e bu
ildi
ng
code
.
3.LI
VES
TOC
KD
uri
ng
the
win
ter,
a h
orse
requ
ires
abo
ut
36 l
iter
s of
wat
er p
er d
ayan
d a
shee
p re
quir
es a
bou
t 3.
6 li
ters
pe
r da
y. A
farm
er i
s ab
le t
o su
pply
h
is h
orse
s an
d sh
eep
wit
h a
tot
al o
f 30
0 li
ters
of
wat
er e
ach
day
. Wri
te a
nin
equ
alit
y th
at r
epre
sen
ts t
he
poss
ible
nu
mbe
r of
hor
ses
and
shee
p th
is f
arm
erca
n k
eep.
36h
�3.
6s
300
4.W
EIG
HT
Ade
live
ry c
rew
is
goin
g to
loa
da
tru
ck w
ith
tab
les
and
chai
rs.
Th
e tr
uck
s w
eigh
t li
mit
atio
ns
are
repr
esen
ted
by t
he
ineq
ual
ity
200t
�60
c�
1200
, wh
ere
tis
th
en
um
ber
of t
able
s an
d c
is t
he
nu
mbe
r of
ch
airs
. Gra
ph t
his
in
equ
alit
y.
AR
TF
or E
xerc
ises
5–7
, use
th
efo
llow
ing
info
rmat
ion
.
An
art
ist
can
sel
l ea
ch d
raw
ing
for
$100
and
each
pai
nti
ng
for
$400
. He
hop
es t
om
ake
at l
east
$20
00 e
very
mon
th.
5.W
rite
an
in
equ
alit
y th
at e
xpre
sses
how
man
y pa
inti
ngs
an
d/or
dra
win
gs t
he
arti
st n
eeds
to
sell
eac
h m
onth
to
reac
hh
is g
oal.
100d
�40
0p�
2000
6.G
raph
th
e in
equ
alit
y.
7.If
Dav
id s
ells
th
ree
pain
tin
gs o
ne
mon
th, h
ow m
any
draw
ings
wou
ld h
eh
ave
to s
ell
in t
he
sam
e m
onth
to
reac
h$2
000?
8
p
dO2 14 36 589 7
812
416
2428
2032
36
2 14 36 589 7
812
416
2428
2032
36
t
cO
Tables
Ch
airs
y
x
100
120 80 60 40 20 0
23
14
56
7
Height (ft)
Dis
tan
ce f
rom
Par
k C
ente
r(h
un
dre
d f
t)
w
�O2530 20 15 10 5
2530
510
1520
Wor
d Pr
oble
m P
ract
ice
Gra
ph
ing
Ineq
ual
itie
s
Lesson 2-7
Cha
pter
255
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
Lim
its
Th
e co
nce
pt o
f th
e li
mit
is
cen
tral
to
man
y ar
eas
of m
ath
emat
ics,
esp
ecia
lly
to c
alcu
lus.
F
orex
ampl
e, c
onsi
der
the
expr
essi
on, 3
x�2.
As
the
valu
e of
xap
proa
ches
1, t
he
valu
e of
th
eex
pres
sion
app
roac
hes
5, a
s sh
own
in
th
e ta
ble
belo
w.
Th
e pr
oces
s of
sys
tem
atic
ally
choo
sin
g va
lues
clo
ser
to 1
an
d pr
odu
cin
g va
lues
clo
ser
to 5
dem
onst
rate
s fi
ndi
ng
the
lim
itof
th
e ex
pres
sion
.
Fin
d t
he
lim
its
for
each
exp
ress
ion
as
xap
pro
ach
es t
he
valu
e gi
ven
.
1.2x
�2
as x
appr
oach
es 5
2.x
�5
as x
appr
oach
es 1
112
6
3.as
xap
proa
ches
14.
as x
appr
oach
es 1
�
5.as
xap
proa
ches
100
6.as
xap
proa
ches
100
�3.
24�
4.93
7.as
xap
proa
ches
100
08.
as x
app
roac
hes
100
0
�3.
02�
4.99
9.W
hat
do
you
not
ice
abou
t th
e li
mit
s yo
u f
oun
d in
exe
rcis
es 3
–8?
In t
he
firs
t se
t,th
e lim
it is
ap
pro
ach
ing
3 a
s x
incr
ease
s.In
th
e se
con
dse
t,th
e lim
it is
ap
pro
ach
ing
5 a
s x
incr
ease
s.
4998
� 1001
3005
� 994
5x�
2� x
�1
3x�
5� x
�6
498
� 101
305
� 94
5x�
2� x
�1
3x�
5� x
�6
3 � 28 � 5
5x�
2� x
�1
3x�
5� x
�6
x3x
�2
0.90
04.
700
0.95
04.
850
0.99
04.
970
0.99
94.
997
0.99
994.
9997
A1-A26 A2-02-873972 5/17/06 10:37 AM Page A26
