Slope

Supplement 2

Find a slope

Graphing with Slope

Slope

Slope describes the direction of a line.

Guard against 0 in the

denominator

SlopeIf x1 x2, the slope of the line

through the distinct points (x1, y1) and (x2, y2) is

12

12

xx

yy

xinchange

yinchange

run

risem

Why is this

needed?

x-axis

y-axis

Find the slope between (-3, 6) and (5, 2)

RiseRun

-48

-12

= =

Find the slope between(-3, 6) and (5, 2)

12

12

xx

yym

)3()5(

)6()2(

m8

4

2

1

Find the Slope

(5, -2)

(11, 2)

(3, 9)

12

12

xx

yym

1

2 9

11 3m

Green

511

)2(22

m

Blue

3

2 9

5 3m

Red

7

8

3

2

11

2

Find the slope between (5, 4) and (5, 2).

12

12

xx

yym

)5()5(

)4()2(

m0

2 STOP

This slope is undefined.

x-axis

y-axis

Find the slope between (5, 4) and (5, 2).

RiseRun

-20

Undefined= =

Find the slope between(5, 4) and (-3, 4).

12

12

xx

yym

)5()3(

)4()4(

m8

0

STOP

This slope is zero.

x-axis

y-axis

Find the slope between (5, 4) and (-3, 4).

RiseRun

0-8

Zero= =

From these results we can see...

• The slope of a vertical line is undefined.

• The slope of a horizontal line is 0.

x-axis

y-axis

Graph the line that goes through (1, -3) with

(1,-3)

4

3m

Using Slope to Graph

• Graph the line that contains (4, 5) and has a slope of 3/2.

(4, 5)

(6, 8)

(8, 11)

Using Slope to Graph

• Graph

(0, 8)

(4, 5)

(8, 2)

38

4y x

Slope Worksheet 10 points

Find the slope of the lines that contain the following pairs of points.

a. (2, 3) and (-4, -5)

b. (0, 0) and (2, 3)

c. (3, 0) and (7, 4)

d. (7, 4) and (3, 0)

e. (2, 3) and (2, -5)

Sketch a graph of the following lines.

1. y = 4x – 8

2. y = -3x + 6

3.

4.

5.

38

4y x

26

3y x

12

5y x