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Holt Algebra 1
5-8 Slopes of Parallel and Perpendicular Lines
Warm UpIdentify which lines are parallel.
1.y = 6; y = 6x + 5; y = 6x – 7; y = -8
Identify which lines are perpendicular2.y = 3x – 4; y = x + 2; y = -1; x = 3
Holt Algebra 1
5-8 Slopes of Parallel and Perpendicular Lines
Identify and graph parallel and perpendicular lines.
Write equations to describe lines parallel or perpendicular to a given line.
Objectives
Holt Algebra 1
5-8 Slopes of Parallel and Perpendicular Lines
Vocabularyparallel linesperpendicular 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.
y = 3x + 8 The slope is 3.
The parallel line also has a slope of 3.
Step 2 Write the equation in point-slope form.
Use the point-slope form.y – y1 = m(x – x1)
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
Distribute 3 on the right side.
Add 10 to both sides.
Holt Algebra 1
5-8 Slopes of Parallel and Perpendicular Lines
Example 2
y = x – 6; (5, 7)
Step 1 Find the slope of the line.
Step 2 Write the equation in point-slope form.
Use the point-slope form.
y = x –6 The slope is .
The parallel line also has a slope of .
y – y1 = m(x – x1)
Holt Algebra 1
5-8 Slopes of Parallel and Perpendicular Lines
Example 2 Continued
Step 3 Write the equation in slope-intercept form.
Add 7 to both sides.
Distribute on the right side.
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.
y = 2x – 5 The slope is 2.
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)
Substitute for m, –1 for y1,
and 2 for x1.
Holt Algebra 1
5-8 Slopes of Parallel and Perpendicular Lines
Step 3 Write the equation in slope-intercept form.
Distribute on the right side.
Subtract 1 from both sides.
Example 3 Continued
Holt Algebra 1
5-8 Slopes of Parallel and Perpendicular Lines
Example 4y = 5x; (–5, 3)
Step 1 Find the slope of the line.y = 5x The slope is 5.
Step 2 Write the equation in point-slope form.Use the point-slope form.
The perpendicular line has a slope of because
.
y – y1 = m(x – x1)
Holt Algebra 1
5-8 Slopes of Parallel and Perpendicular Lines
Step 3 Write in slope-intercept form.
Add 3 to both sides.
Distribute on the right side.
Example 4 Continued
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
