1. Chapter 3 Introduction to Graphing and Equations of Lines
Section 6
Parallel and Perpendicular Lines

2. Section 3.6 Objectives 1 Determine Whether Two Lines Are Parallel
2 Find the Equation of a Line Parallel to a Given Line
3 Determine Whether Two Lines Are Perpendicular
4 Find the Equation of a Line Perpendicular to a Given Line

3. Parallel Lines
Two nonvertical lines are parallel if and only if their slopes are equal and they have different y-intercepts. Vertical lines are parallel if they have different x-intercepts. x y x y
m1 = m2
m1 = m2

4. Parallel Lines Example:
Determine whether the line 6x + 2y = 9 is parallel to – 3x – y = 3.
Find the slope of each line.
6x + 2y = 9
– 3x – y = 3
The slopes are the same so the lines are parallel.

5. Parallel Lines Example:
Find the equation of the line that is parallel to 4x + y = – 8 and contains the point (2, – 3). Write the equation in slope-intercept form.
Find the slope of the line.
4x + y = – 8
y = – 4x – 8
Use the point-slope form to find the equation.
Substitute in the values.
Simplify.
Subtract 3 from both sides.

6. Perpendicular Lines m1m2 =  1 or m1 =
Two nonvertical lines are perpendicular if and only if the product of their slopes is – 1. Any vertical line is perpendicular to any horizontal line. x y
m1m2 =  1 or
The slopes are negative reciprocals of each other.
m1 =

7. Perpendicular Lines Example:
Determine whether the line x + 3y = – 15 is perpendicular to
– 3x + y = – 1 .
Find the slope of each line.
x + 3y = – 15
– 3x + y = – 1
The slopes are negative reciprocals so the lines are perpendicular.

8. Perpendicular Lines Example:
Find the equation of the line that is perpendicular to the line – 2x + 5y = 3 and contains the point (2, – 3). Write the equation in slope-intercept form.
Find the slope of the line.
– 2x + 5y = 3
5y = 2x + 3
Continued.

9. Perpendicular Lines Example continued:
Use the point-slope form to find the equation.
Use the negative reciprocal slope.
Simplify.
Subtract 3 from both sides.