Simplify. Exercise 4 − 2 5 − 2 2323 2323. Simplify. 5 − 2 4 − 2 3232 3232 Exercise.

Simplify.Simplify.ExerciseExercise

4 − 25 − 24 − 25 − 2

2323

Simplify.Simplify.

5 − 24 − 25 − 24 − 2

3232

ExerciseExercise

Simplify.Simplify.

2 − 45 − 22 − 45 − 2

ExerciseExercise

2323

– –

Simplify.Simplify.

2 − 42 − 52 − 42 − 5

2323

ExerciseExercise

Simplify.Simplify.

2 − 25 − 22 − 25 − 2 00

ExerciseExercise

Simplify.Simplify.

4 − 22 − 24 − 22 − 2 undefinedundefined

ExerciseExercise

The rise is the vertical change from point P1 to point P2 on a line.

The rise is the vertical change from point P1 to point P2 on a line.

RiseRise

The run is the horizontal change from point P1 to point P2 on a line.

The run is the horizontal change from point P1 to point P2 on a line.

RunRun

The slope of a line is the ratio of the rise to the run. The variable m is often used for slope.

The slope of a line is the ratio of the rise to the run. The variable m is often used for slope.

SlopeSlope

yy

xx

yy

xx

up to right positive

down to right negative

horizontal zero

vertical undefined

SlopeSlope

Slope = m = Slope = m = riserunriserun

yy

xx−3−3

1 1

Find the slope of the given line.Find the slope of the given line.

m = = −3m = = −3−31

−31

Example 1Example 1

If a line contains the points P2 (x2, y2) and P1 (x1, y1),

then m = vertical change y2 − y1 horizontal change x2 − x1

vertical change y2 − y1 horizontal change x2 − x1

==

Slope FormulaSlope Formula

Find the slope of the line that contains the points (1, 2) and (7, 5).

Find the slope of the line that contains the points (1, 2) and (7, 5).

m = =m = =y2 − y1 x2 − x1 y2 − y1 x2 − x1

5 − 2

7 − 1

5 − 2

7 − 1== 3636

== 1212

Example 2Example 2

Find the slope of CD passing through (5, 3) and (2, 5).Find the slope of CD passing through (5, 3) and (2, 5).

m = =m = =y2 − y1 x2 − x1 y2 − y1 x2 − x1

5 − 3

2 − 5

5 − 3

2 − 5== 2−32

−3= −= − 2

323

Example 3Example 3

Find the slope of EF passing through (3, 2) and (−1, 2).Find the slope of EF passing through (3, 2) and (−1, 2).

m = =m = =y2 − y1 x2 − x1 y2 − y1 x2 − x1

2 − 2 −1 − 32 − 2

−1 − 3

== 0−40

−4= 0= 0

Example 4Example 4

yy

xx

(−1, 2)(−1, 2) (3, 2)(3, 2)

== 4040

Find the slope of the line passing through the points (2, 1) and (2, 5).

Find the slope of the line passing through the points (2, 1) and (2, 5).

m = =m = =y2 − y1 x2 − x1 y2 − y1 x2 − x1

5 − 1

2 − 2

5 − 1

2 − 2

Example 5Example 5

yy

xx

(2, 5)(2, 5)

(2, 1)(2, 1)

m = 3m = 3

Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.

y = 3x + 5y = 3x + 5

ExampleExample

1212

y = − x + 2y = − x + 2

Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.

m = −m = − 1212

ExampleExample

2323

y = x − 1y = x − 1

Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.

m = m = 2323

ExampleExample

m = 0m = 0

Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.

y = 4y = 4

ExampleExample

m = −3m = −3

Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.

y = −3x + 6y = −3x + 6

ExampleExample

undefinedundefined

Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.

x = 4x = 4

ExampleExample

They are the same.They are the same.

Compare the slopes of the lines in the previous questions to the coefficients of x.

Compare the slopes of the lines in the previous questions to the coefficients of x.

ExampleExample

m =m = 5252

Find the slope of the line through (3, 7) and (5, 12).Find the slope of the line through (3, 7) and (5, 12).

ExampleExample

m = −6m = −6

Find the slope of the line through (2, 3) and (4, −9).Find the slope of the line through (2, 3) and (4, −9).

ExampleExample

m = 0m = 0

Find the slope of the line through (2, 5) and (3, 5).Find the slope of the line through (2, 5) and (3, 5).

ExampleExample

m = undefinedm = undefined

Find the slope of the line through (1, 1) and (1, 2).Find the slope of the line through (1, 1) and (1, 2).

ExampleExample

Their slopes are the same and the lines are parallel.Their slopes are the same and the lines are parallel.

Graph the following lines and describe their graphs: y = 3x − 4, y = 3x, and y = 3x + 2.

Graph the following lines and describe their graphs: y = 3x − 4, y = 3x, and y = 3x + 2.

ExampleExample