Section 6.5:Parallel and Perpendicular Lines

Objectives:• Determine whether lines are parallel• Determine whether lines are perpendicular• Write equations of parallel and perpendicular

lines

Property: Slopes of Parallel Lines

Non-vertical lines are parallel if they have the same slope and different y-intercepts.

Any two vertical lines are parallel

Are the following lines parallel?

1) y = 5x + 5; y = 5x – 10

2) y = -x; y – 3 = -1(x + 9)

3) 4x + 2y = 6; -6x + 3y = 1

Find the slope of the line parallel to the graph of each equation.

1) y = 4x + 2 2) y = -9x – 13

3) y – 3 = 0 4) -5x + 5y = 4

Writing equations of || lines

• Write an equation of a line || to y = 3x + 2 and passes through the point (-1, 4)

Writing equations of || lines

• Write an equation of a line || to y = ½ x + 2 and passes through the point (6, -3)

Property: Slopes of Perpendicular Lines

Two lines are perpendicular if the product of their slopes is -1. That is, if their slopes are opposite reciprocals.

A vertical and a horizontal line are also perpendicular

Are the following lines perpendicular?

1) y = 6x; y = -1/6x + 2

2) y = 3x – 2; 3y = -x – 11

3) y = -5x + 7; y = -1/5x + 2

Find the slope of the line perpendicular to the graph of each equation

1) y = 2/3x – 4 2) y – 4 = -7(x + 2)

3) x – 6y = 15 4) 3y = -x -11

Writing equations of | lines

• Write an equation of a line that is | to y – 2 = 2(x + 3) and passes through the point (6, -1)

Writing equations of | lines

• Write an equation of a line that is | to and passes through the point (6, -1)