Constant Rate of Change and Slope

9.3

Rate of Change

• Rate of Change: describes how a quantity changes in relation to another

• Constant Rate of Change: The rate of change is the same between any two point.

• All Linear Functions have a Constant Rate of Change

Find the Constant Rate of Change in the table

Hours (x)

1 2 3 4

Feet (y)

-12 -14 -16 -18

+1 +1 +1

-2 -2 -2change in y

change in x

2

1

Slope

vertical change risem

horizontal change run

Meet Joe….Joe Cool

• Joe has a disease, he can only walk to the right.

• Use Joe to help you find the slope

• Always start on the left to help Joe walk to the right

5

4

3

2

1

-1

-2

-3

-4

-5

-6 -4 -2 2 4 6 8

“slope”

x"" in change

y"" in changeslope

2

3 run

rise

5

4

3

2

1

-1

-2

-3

-4

-5

-6 -4 -2 2 4 6 8

Graph the line containing the points (-4,2) and (2,-3) and find the slope.

x"" in change

y"" in changeslope

5

6

Slope of a Horizontal line (y=#)

Always 0

What is the slope?

(5,4)(-6,4)

Horizontal line = “0” slope

2 1

2 1

y y

xm

x

Slope of a Vertical Line (x=#)

Always Undefined

What is the slope?

(3,8)

(3,-2)

Vertical line = “no slope”

2 1

2 1

y y

xm

x

Slope Formula

1, 1 2 2: ( ) ( , )given x y and x y

2 1

2 1

y ym

x x

Find the slope of the line containing (2,2) and (8,9)

2 1

2 1

("m")y y

slopex x

9-2 = 7 8-2 6

Find the slope of the line containing (-4,-6) and (3,-2)

M= -2 - -6 = -2 + 6 = 4 3 - -4 3 + 4 7

2 1

2 1

("m")y y

slopex x

Find the slope of the line containing (1,1) and (3,5)

5 1

3 1m

4 2

2 1

2 1

2 1

("m")y y

slopex x

Adventures of Slope Dude

• http://www.youtube.com/watch?v=ZzU8x5cMR-w

Homework

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