M. Pickens 2006

Slope

M. Pickens 2006

8.4 Rate of Change & Slope

• To learn what slope is• To learn what a line looks like when

it has positive, negative, zero or undefined slope

• To learn how to find the slope of a graph

• To learn how to find the slope of a table

M. Pickens 2006

What is Slope?Slope is the rate of change of a line.It indicates the steepness of the line.

runriseslope x

yslope

(change in y)(change in x)

12

12

xxyyslope

M. Pickens 2006

What does the line look like when…

• You have positive slope?

• You have negative slope?

• You have zero slope?

• You have NO slope?

M. Pickens 2006

Slope MountainSki Resort

Positive slope, + work

Negative slope, - work

Zero slope is zero fun!

NO slope.

Oh No!!!!

T. Merrill 2005

M. Pickens 2006

What Type of Slope is Shown?

Positive SlopeNegative Slope

Zero SlopeNo Slope/Undefined

M. Pickens 2006

Slope of a Graph• When slope is positive or negative

we need to find the actual value of the slope or rate of change

• On a graph we find slope using the formula

runriseslope

How far up or down it changes

How far left or right it changes

M. Pickens 2006

Slope of a Graph

1.First pick two points on the lineThe points need to be where the lines cross so they are integers

2. Then find the rise and run

3. Determine if the slope of the line is positive or negative

Rise = 2Run = 3

runriseslope

32

M. Pickens 2006

Slope of a Graph

1.First pick two points on the lineThe points need to be where the lines cross so they are integers

2. Then find the rise and run

3. Determine if the slope of the line is positive or negative

Rise = 10

Run = 2

runriseslope

210

5

M. Pickens 2006

Slope of a Graphed Line

Find the slope of each line below

x

ySlopes:

RUNRISE

11

44

4

4

Find the slope of each line below

060

14

28

43

undefined02

M. Pickens 2006

Slope of a Table• In a table we can use the same formula.

Pick any two pairs in the table for coordinates

x y-4 -171 -23 48 19

10 25

Pick any two rows. If it is linear it will be the same

no matter which two rows you pick

xyslope

change? x value thedid Howchange? y value thedid How

slope

2by increase

6by increase

26

3

M. Pickens 2006

Slope of a Table

• Find the slope for each table below

x y-3 4.25-1 2.750 21 1.255 -

1.75

x y-8 2-6 3-3 4.5-1 5.50 6

xyslope

2 increase1.5 decrease

25.1

fraction)in decimal (no43

xyslope

2by increase1by increase

21

M. Pickens 2006

Conclusion• Slope is:

• Describe the slope of each of the following

the rate of change of a line

runriseslope

xyslope

Negative slope Undefined/ No slope

Positive slope Zero/0 slope