Parallel & Perpendicular Lines

Parallel Lines

m = 2/1

m = 2/1

What is the slope of the 2nd line?

+1

+2

+1

+2

Perpendicular Lines

m = 2/1

What is the slope of the 2nd line?

+1

+2

+2

-1

m = -1/2

Parallel : Same Slope

Perpendicular : Opposite Reciprocal Slope

m = 2/1 m = 2/1

m = 2/1 m = -1/2

Perpendicular : Opposite Reciprocal Slope

m = -2/1 m = +1/2

m = +1/3 m = -3/1

Find the equation for the lineparallel to 2x + y = 6

and passing through ( 2 , -3 )

First, we need slope and a point:

2x + y = 6

y = -2x + 6

m = -2 Point: ( 2 , -3 )

With… slope -2 and point (2 ,-3)

y = -2x + b

-3 = -2(2) + b

y = -2x + 1

Find the equation for the lineperpendicular to x + 3y = 6

and passing through ( 1 , -2 )

First, we need slope and a point:x + 3y = 6

3y = -1x + 6

m = -1/3

Point: ( 1 , -2 )

y = -1/3(x) + 2

But perpendicular, so +3/1

With… slope 3 and point (1 ,-2)

y = 3x +b

-2 = 3(1) + b

y = 3x - 5