Chapter 4

Unit Question

How do we graph in algebra?

Open Learning Logs

Date on Left…Section 4 – 8 on right

Warm – Up Section 4 – 8

Tell in which quadrant or on which axis the point lies…

X – coordinate Y - coordinate

Positive Negative

Negative Negative

Negative Positive

0 Positive

Positive Positive

Negative 0

Section 8

How do we calculate size changes in geometry?

Homework Clicky

Size change model for multiplication…

Let k be a nonzero number without a unit. Then

kx is the result of applying a size change of

magnitude k to the quantity x.

Types of size changes:

EXPANSION CONTRACTION

k > 1 OR k < -1 -1 < k < 1

“Outside the ones” “Between the ones”

-4 -3 -2 -1 0 1 2 3 4

Graph the points…

A = ( 0 , 2 )

B = ( 2 , 1 )

C = ( 3 , 5 )

EXPANSION BY 2

A’ = 2( 0 , 2 )

B’ = 2( 2 , 1 )

C’ = 2( 3 , 5 )

= ( 0 , 4 )

= ( 4 , 2 )

= ( 6 , 10 )

Graph counts by twos

Positive expansions get bigger!

Graph the points…

A = ( 0 , 2 )

B = ( 2 , 1 )

C = ( 3 , 5 )

EXPANSION BY -2

A’ = -2( 0 , 2 )

B’ = -2( 2 , 1 )

C’ = -2( 3 , 5 )

= ( 0 , -4 )

= ( -4 , -2 )

= ( -6 , -10 )

Graph counts by twos

Negative expansions get bigger and “do a double flip”

Graph the points…

A = ( 0 , 1 )

B = ( 2 , 1 )

C = ( 4 , 3 )

CONTRACTION of magnitude -½

A’ = -½ ( 0 , 1 )

B’ = -½ ( 2 , 1 )

C’ = -½ ( 4 , 3 )

= ( 0 , -½ )

= ( -1 , -½ )

= ( -2 , -1½ )

Graph counts by ones

Negative contractions get smaller and “do a double flip”

Frank receives time and a half for overtime. If his overtime rate is $28.28, what is his normal wage?

28.285.1 x5.1 5.1

85.18x

Frank’s Wage is experiencing an expansion of 1.5…

If we let x = Frank’s Wage

Then 1.5x = his overtime wage

Frank’s normal wage is about $18.85/hour

Since I love to photocopy, I take a picture of dimensions 6cm by 8cm, reduce by 60% and then enlarge by 125%.

What are the new dimensions?

1st do the reduction

60% = 0.60

6 • 0.60 = 3.6

8 • 0.60 = 4.8

The picture is 3.6cm by 4.8 cm

after the reduction

2nd do the expansion

125% = 1.25

3.6 • 1.25 = 4.5

4.8 • 1.25 = 6

The picture is 4.5 cm by 6 cm

after the expansion

Can we combine them?

Reduce 60% = -60

Enlarge by 125% = +125

-60 + 125 = +65%

We CANNOT combine

Percents this way!!!!

6 • 0.65 = 3.9

8 • 0.65 = 5.2

Homework

• Do HoffmaSheet 4 – 8