1. 5-5 Parallel and Perpendicular Lines
Hubarth
Algebra

2. Parallel Lines are in the same plane and never intersect.
Slopes of Parallel Lines
Nonvertical lines are parallel if they have the same slope and different y-intercepts.
Any two vertical lines are parallel.
Example The equation y = 2 3 x + 1 and y = 2 3 x – 3 have the same slope, 2 3 , and different
y-intercepts. The graphs of the two equations are parallel.
*Key* Parallel lines have the same slope different y-intercepts.

3. Ex 1 Determining Whether Lines are Parallel
Are the graphs of y = –2x – 1 and 4x + 2y = 6 parallel?
Write 4x + 2y = 6 in slope-intercept form. Then compare
with y = –2x – 1.
2y = –4x + 6 Subtract 4x from each side.
Divide each side by 2.
2y –4x + 6 =
y = –2x + 3 Simplify.
The lines are parallel. The equations have the same
slope, –2, and different y-intercepts.

4. Ex 2 Writing Equations of Parallel Lines5 2
Write an equation for the line that contains (–2, 3) and is parallel to y = x – 4. 5 2
Step 1  Identify the
slope of the
given line.
y = x – 4
slope
Step 2  Write the equation of the line through (–2, 3)
using point-slope form.
y – y1 = m(x – x1) Use point-slope form.
y – 3 = (x + 2) Substitute (–2, 3) for (x1, y1) and for m. 5 2
Now change to slope-intercept form
y – 3 = x + (2) Use the Distributive Property. 5 2
y – 3 = x Simplify. 5 2
y = x Add 3 to each side
and simplify. 5 2

5. Perpendicular Lines are lines that intersect to form a right angle.
Slope of Perpendicular lines
Two lines are perpendicular if the product of their slopes is -1. Also, the slopes will be the
negative reciprocal of each other. A vertical and a horizontal line are also perpendicular.
Example the negative reciprocal will be , -5 the negative reciprocal will be 1 5
Example The slope of y = x – 1 is The slope of y = 4x + 2 is 4.
The negative reciprocal of is or 4, so the two equations form perpendicular lines.
*Key – perpendicular lines slopes are the negative reciprocal of each other

6. Ex 3 Writing Equations for Perpendicular Lines
Write an equation of the line that contains (6, 2) and is perpendicular to y = –2x + 7.
Step 1 Identify the slope of the given line, y = – 2 x + 7
m = -2
Step 2  Find the negative reciprocal of the slope.
The negative reciprocal of –2 is . 1 2
Step 3  Use the slope-intercept form to write an equation.
y = mx + b 1 2
2 = (6) + b Substitute for m, 6 for x, and 2 for y.
2 = 3 + b Simplify.
2 – 3 = 3 + b – Subtract 3 from each side.
–1 = b Simplify.
The equation is y = x – 1. 1 2

7. Practice
1. Are the graphs of -6x + 8y =-24 and y = 3 4 x -7 parallel? Explain.
Yes, same slope, different intercepts
2. Write an equation for the line that contains (2, -6) and is parallel to y = 3x + 9.
y = 3x -12
3. Write an equation of the line that contains (1, 8) and is perpendicular to y = 3 4 x + 1.
y = 4 3 x