5-8
Slopes of Parallel and
Perpendicular Lines
Warm Up
Identify which lines are parallel.
1. y = 6;
y = 6x + 5;
y = 6x – 7;
y = -8
Identify which lines are perpendicular
2. y = 3x – 4; y =
x + 2; y = -1; x = 3
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Objectives
Identify and graph parallel and perpendicular
lines.
Write equations to describe lines parallel or
perpendicular to a given line.
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Vocabulary
parallel lines
perpendicular lines
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Directions:
Write an equation in slope-intercept
form for the line that is parallel to the
given line and that passes through the
given point.
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Example 1
y = 3x + 8;
(4, 10)
Step 1 Find the slope of the line.
The slope is 3.
y = 3x + 8
The parallel line also has a slope of 3.
Step 2 Write the equation in point-slope form.
y – y1 = m(x – x1)
Use the point-slope form.
y – 10 = 3(x – 4)
Substitute 3 for m, 4
for x1, and 10 for y1.
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Example 1 Continued
Step 3 Write the equation in slope-intercept form.
y – 10 = 3(x – 4)
y – 10 = 3x – 12)
y = 3x – 2
Holt Algebra 1
Distribute 3 on the right side.
Add 10 to both sides.
Slopes of Parallel and
Perpendicular Lines
5-8
Example 2
y=
x – 6;
(5, 7)
Step 1 Find the slope of the line.
y=
x –6
The slope is
The parallel line also has a slope of
.
.
Step 2 Write the equation in point-slope form.
y – y1 = m(x – x1)
Holt Algebra 1
Use the point-slope form.
5-8
Slopes of Parallel and
Perpendicular Lines
Example 2 Continued
Step 3 Write the equation in slope-intercept form.
Distribute
on the right side.
Add 7 to both sides.
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Directions:
Write an equation in slope-intercept
form for the line that is perpendicular
to the given line and that passes
through the given point.
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Example 3
y = 2x – 5;
(2, –1).
Step 1 Find the slope of the line.
The slope is 2.
y = 2x – 5
The perpendicular line has a slope of
because
Step 2 Write the equation in point-slope form.
Use the point-slope form.
y – y1 = m(x – x1)
Holt Algebra 1
Substitute
and 2 for x1.
for m, –1 for y1,
5-8
Slopes of Parallel and
Perpendicular Lines
Example 3 Continued
Step 3 Write the equation in slope-intercept form.
Distribute
on the right side.
Subtract 1 from both sides.
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
y = 5x;
(–5, 3)
Example 4
Step 1 Find the slope of the line.
The slope is 5.
y = 5x
The perpendicular line has a slope of
because
.
Step 2 Write the equation in point-slope form.
y – y1 = m(x – x1)
Use the point-slope form.
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Example 4 Continued
Step 3 Write in slope-intercept form.
Distribute
side.
on the right
Add 3 to both sides.
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Lesson Summary
Write an equation is slope-intercept form
for the line described.
1. contains the point (8, –12) and is parallel to
2. contains the point (4, –3) and is perpendicular
to y = 4x + 5
Holt Algebra 1