7/21/2019 Chapter 2_linear Law

http://slidepdf.com/reader/full/chapter-2linear-law 1/5

CHAPTER 2

₡HAPTER 2 : LINEAR LAW

A. REVISION

 y=mx+c

EXAMPLE 1

Given that point A (2,4) and point B (8,!)" A #ine i$ %ointed &'o thi$ point" ind

the e*+ation o& the #ine"

B. DRAWING THE BEST FITTED LINE

A #ine o& e$t -t i$ pa$$ tho+.h a## point$ o' the n+e' o& point$ a#an/e on oth

o& the #ine

Impotant !!! Logs "#$ R#%# to t&# %om"a$

EXAMPLE ' (SPM ')11*P'+,-

 Ta#e $ho0$ va#+e$ o& t0o va'ia#e$, 1 and , otained &'o an e1pe'ient"

3a'ia#e$ 1 and a'e 'e#ated the e*+ation

n

 y

= px+1

, 0he'e n and p a'e

/on$tant$"

a) Ba$ed on the ta#e /on$t'+/t a ta#e &o' the va#+e o& 1

 y "

/ !" !"2 !" !"4 !"5 !"60 !"!

!"6

4

!"46

5

!"58

8

!"7!

7

"8

8

7/21/2019 Chapter 2_linear Law

http://slidepdf.com/reader/full/chapter-2linear-law 2/5

CHAPTER 2

) P#ot1

 y  

a.ain$t 1,

+$in. the $/a#e o&

2/ to !" +niton the 1a1i$

and 2 / to !"5

+nit$ on the1

 y

a1i$" Hen/e,

d'a0 the #ine o&

e$t -t"/) 9$e the .'aph in

() to -nd theva#+e o&  

i 0hen the

va#+e o& 1 ;!"8

iin

iiip

. on2#t3ng

%om non4"3n#ato "3n#a

2

 Non-Linear FunctionA) Compare with y=mx+c

by comparing with Y = mX + c

y = ax2 + b

y = ax3 + b

y2 = ax + b

 baxy

1   2+=

 Non-Linear Function b) By using logarithm

by taking log to both sides

y = axx 

y = cakx 

py = qx

yxn  = c

7/21/2019 Chapter 2_linear Law

http://slidepdf.com/reader/full/chapter-2linear-law 3/5

CHAPTER 2

EXAMPLE 5

 The dia.'a e#o0 $ho0 that a pa't o& the .'aph o& x

 y  a.ain$t 1" The va'ia#e

1 and a'e 'e#ated to the e*+ation  px+qy= xy , 0he'e p and * a'e /on$tant"

ind the va#+e o& p and *"

EXAMPLE 6

 x

 y

(,8

4 2

 x 

7/21/2019 Chapter 2_linear Law

http://slidepdf.com/reader/full/chapter-2linear-law 4/5

CHAPTER 2

 The dia.'a e#o0 $ho0 that a pa't o& the .'aph o&log10 y a.ain$t

  log10  x "

Given that  yx=108.  Ca#/+#ate va#+e o& < and h"

,7ESTION 1

 Ta#e $ho0$ va#+e$ o& t0o va'ia#e$, 1 and , otained &'o an e1pe'ient"

3a'ia#e$ 1 and a'e 'e#ated the e*+ation   y=h x

k  , 0he'e h and < a'e

/on$tant$"

a) Ba$ed on the ta#e /on$t'+/t a ta#e &o' the va#+e o&   log10 y "

) P#otlog10 y  a.ain$t 1, +$in. the $/a#e o& 2/ to +nit on the 1a1i$ and 2

/ to !" +nit$ on thelog10 y  a1i$" Hen/e, d'a0 the #ine o& e$t -t"

4

log10 y

(2,<

(h,

log10  x

X 4 5 6 = 8 8  2"5= " 4"!= 4"7! 6" ="74

7/21/2019 Chapter 2_linear Law

http://slidepdf.com/reader/full/chapter-2linear-law 5/5

CHAPTER 2

/) 9$e the .'aph in () to -nd the va#+e o& 

i 0hen the va#+e o& 1 ;2"= iih iii<

,7ESTION '

 Ta#e $ho0$ va#+e$ o& t0o va'ia#e$, 1 and , otained &'o an e1pe'ient"

3a'ia#e$ 1 and a'e 'e#ated the e*+ationk 

 y= p

 x+1

, 0he'e h and < a'e

/on$tant$"

a) Ba$ed on the ta#e /on$t'+/t a ta#e &o' the va#+e o& 1

 x  and1

 y "

) P#ot1

 y  a.ain$t1

 x , +$in. the $/a#e o& 2/ to !" +nit on the1

 x a1i$

and 2 / to !"5 +nit$ on the1

 y  a1i$" Hen/e, d'a0 the #ine o& e$t -t"

/) 9$e the .'aph in () to -nd the va#+e o& 

i < iip

,7ESTION 5

 Ta#e $ho0$ va#+e$ o& t0o va'ia#e$, 1 and , otained &'o an e1pe'ient"

3a'ia#e$ 1 and a'e 'e#ated the e*+ation   y=hk 2 x

, 0he'e h and < a'e

/on$tant$"

a) P#otlog10 y  a.ain$t   x , +$in. the $/a#e o& 2/ to +nit on the  x a1i$

and 2 / to !" +nit$ on thelog10 y  a1i$" Hen/e, d'a0 the #ine o& e$t -t"

) 9$e the .'aph in () to -nd the va#+e o& 

i 1 0hen the va#+e o& ;4"8 iih iii<

5

X "5 2"! "! 4"! 5"! 6"! 8  2"5!

2

!"==

!

!"46

5

!"8

5

!"5

!"2

8

X "5 "! 4"5 6"! ="5 7"! 8  2"5 "24 4"= 5"=5 ="=6 !"!

!