Slope of a Line

Chapter 7.3

Slope of a Line

m = y2 – y1

x2 – x1

m = riserun m =

change in ychange in x

Given two points (x1, y1) and (x2, y2)

There are three ways to describe the slope (m) of a line.

Positive Slope

Lines going up to the right.

Negative Slope

Lines going down to the right.

Zero Slope

Horizontal lines.

No Slope or Undefined Slope

Vertical lines.

m =y2

x2

(x1, y1) (x2, y2)

m = -1-4

m = -2

-10

1. Find the slope of a line that passes through

( , ) and ( , )

m = 15

– y1

– x1

-1-416

––

16

Substitute

Subtract

Simplify

m =y2

x2

(x1, y1) (x2, y2)

m = 1

-1

m = 1

-3

2. Find the slope of a line that passes through

( , ) and ( , )

m = -13

– y1

– x1

1-102

––

02

Substitute

Subtract

Simplify

m =y2

x2

(x1, y1) (x2, y2)

m = 3

-5

m = -30

3a. Find the slope of a line that passes through

( , ) and ( , )

no slope

– y1

– x1

3-56-5

––

6(-5)

Substitute

Subtract

Simplify

or

undefined slope

m =y2

x2

(x1, y1) (x2, y2)

m = -11

3

m = 0

10

3b. Find the slope of a line that passes through

( , ) and ( , )

m =

– y1

– x1

-113-11-7

––

(-11)(-7)

Substitute

Subtract

Simplify

0

Slope-Intercept Form

An equation of a line can be written in slope-intercept form where m is the slope and b is the y-intercept.

y = mx + b

The y-intercept is a point on the y-axis with the coordinates (0, b).

4. Find the slope and y-intercept of a line given the following equation.

4x – 2y = -5

Write in slope-intercept form, y = mx + b

-4x -4x

-2y = -4x – 5-2 -2 -2

y = 2x + 52

m = 2 y-intercept = 52(0, )

5a. Write the equation in slope-intercept form of a line given the following.

Write in slope-intercept form, y = mx + b

y =

-37

slope = y-intercept = 27(0, )

-37 x 2

7+

5b. Write the equation in Standard Form: Ax + By = C.

A, B, and C are integers, and A is positive.

y = -37 x 2

7+7( ) 7( ) 7( )

7y =+3x +3x

-3x + 2

3x + 7y = 2

1 1

Graphing an equation using the Slope-intercept Form

1. May have to rewrite the equation into y = mx + b.

2. Plot the y-intercept (b) on the y-axis.

3. Use the slope to plot 2 more points.

4. Draw a straight line through them.

•

•

•

6. Graph the line with a slope = and a y-intercept = (0, ).

34

1. Plot the y-intercept.

2. Use the slope to plot two more points.

3. Draw the line.

-1

move up 3, right 4.

move down 3, left 4.

••

•

7. Graph the equation: y = x-2

3

1. Plot the y-intercept.

2. Use the slope to plot two more points.

3. Draw the line.

+ 5

move down 2, right 3.

move up 2, left 3.

Slope of a Line

Chapter 7.3