Perpendicular LinesSec 3.7

Goals:To identify perpendicular lines using slopeTo write equations of perpendicular lines

Slope

1y

2x1x

riseslope

run

2y

2 1

2 1

y

x

ym

x

..

2 1 ( )x runx

2 1 ( )y risey

Comparing Slopes of Lines In a coordinate plane, two nonvertical lines are

perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular.

1 2 1m m 1

43

5y x

2

56

4y x

4 51

5 4

1

4

5m

2

5

4m

Examples Decide whether l p

l(5,6)

..

(2,0)

( 2,2).p

lm

2m

Examples Decide whether the lines are perpendicular.

3 2 1x y

6 9 3x y

Writing EquationsFind an equation of a line passing through (3,1)

and perpendicular to line r .

1. Find the slope of a line that is perpendicular to line “r” .

m

m

y mx b

: 3 5r y x

3. Plug and b into

2. Use and the point given to find b.

Students 1. Decide whether the lines are perpendicular.

2. Find an equation passing through (2,-2) and perpendicular to

3. Are the lines with the following points passing through them perpendicular?

Line l (0,7) and (5,2)Line t ( 9,6)and (4,1)

6 2 8x y

3 4y x

110

4y x