3.8 Slopes of Parallel and Perpendicular Lines Slopes of Parallel Lines –If two nonvertical lines...

3.8 Slopes of Parallel and Perpendicular Lines• Slopes of Parallel Lines

– If two nonvertical lines are parallel, then their slopes are equal.

– If the slopes of two distinct nonvertical lines are equal, then the lines are parallel.

– Any two vertical lines or horizontal lines are parallel.

Checking for Parallel Lines• Are lines ℓ1 and ℓ2 parallel? Explain.

Checking for Parallel Lines• Find the slope of each line.

1

2 1

2 1

y ym

x x

5 ( 4)

1 2

9

3

3

2

2 1

2 1

y ym

x x

3 ( 4)

3 ( 1)

7

2

7

2

73

2 NOT

PARALLEL!!!!!!

Writing Equations of Parallel Lines• What is an equation of the line parallel to

y = -3x – 5 that contains (-1 , 8)?

y = -3x – 5

parallel slope = -3

y – y1 = m (x – x1)

y – 8 = -3 (x + 1)

Slopes of Perpendicular Lines

• If two nonvertical lines are perpendicular, then the product of their slopes is -1 (opposite reciprocal).

• If the slopes of two lines have a product of -1, then the lines are perpendicular.

• Any horizontal line and vertical line are perpendicular.

Checking for Perpendicular Lines• Lines ℓ1 and ℓ2 are neither horizontal nor vertical. Are

they perpendicular? Explain.

Checking for Perpendicular Lines• Find the slope of each line.

1

2 1

2 1

y ym

x x

2 ( 4)

4 0

6

4

3

2

2

2 1

2 1

y ym

x x

3 ( 3)

4 ( 5)

6

9

2

3

Perpendicular. The slopes have a product of -1.

Writing Equations of Perpendicular Lines• What is an equation of the line perpendicular to

that contains (15 , -4)? 1

25

y x

5m

1 1( )y y m x x

4 5( 15)y x

More Practice!!!!!

• Homework – Textbook p. 201 – 202 #8 – 20 even.