2.6 Extension Writing Equations of Parallel and Perpendicular Lines.

2.6 ExtensionWriting Equations of

Parallel and Perpendicular Lines

“parallel”

Parallel Lines• Parallel lines have the same exact slope

(“m”) and a different y-intercept (“b”).

•y = 2x +3 and y = 2x +11 are parallel.

• All vertical lines are parallel.

• All Horizontal lines are parallel

y=2 and y =-1 are parallel

x = -5 and x = 9 are parallel.

Determine if the lines are parallel

and1

4 3

x x Y

All vertical lines are parallel.

Determine if the lines are parallel

an2 d11 2 2y x y x

N

1

2

11

2y x

2 2y x

Determine if the lines are parallel

and3 5 5 15 10x y y x

Y

3 5y x 3 2y x 3 5 y x 5 15 10y x

Steps to write an equation of a line that passes through the given point

and parallel to the given line

1.) Identify a parallel slope to the line

2.) Either use slope- intercept or point slope form to write your equation

Write an equation of a line that passes through the given point and parallel to the given line

( 2,1); 3 4y x ( 2,1); 3m

1 3( ( 2))y x 1 3( 2)y x

1 3 6y x 1 1

3 7y x

Perpendicularmeans “at right angles”

All three red lines are perpendicular to the green line.

Slope and Line relationships• Perpendicular lines (): have the

opposite reciprocal slopes•y = 2x + 3 and y =

are perpendicular.

• If you multiply two perpendicular slopes your product will be -1

• All vertical and horizontal lines are perpendicular

6x 1

-2

2 11

1 2

Determine if the lines are perpendicular:

and9 7

1 77 9

y x y x

Y

Determine if the lines are perpendicular:

and7 8

4 78 7

y x y x

NOne must be

positive;

the other negative.

Determine if the lines are perpendicular:

and2 3y x Y

Steps to write an equation of a line that passes through the given point and perpendicular to the given line

1.) Identify a perpendicular slope to the line

2.) Either use slope- intercept or point slope form to write your equation

Write an equation of a line that passes through the given point and perpendicular to the given line

1(4,2); 1

3y x

(4,2); 3m2 3( 4)y x 2 3 12y x 2 2

3 10y x

Homework

RPJ: Page 49-50 (1-16) all