4-7B Perpendicular Lines

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4-7B Perpendicular Lines
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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What is the reciprocal of 8?
What is the opposite reciprocal of 8?
In this lesson you will need to find and use
opposite reciprocals.
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Two lines in a coordinate plane are perpendicular
if they intersect at right angles (90 degree
angles). Horizontal and vertical lines are
perpendicular to each other.
y










x
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In a coordinate plane, two non vertical lines are
perpendicular if and only if the product of their
slopes is 1.
y










x
Do you think these lines are perpendicular?
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How to determine whether lines are perpendicular.
1. Write each line in slope-intercept form.
2. Multiply the slopes together.
3. If the product is 1, then the lines are
perpendicular.
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Write the equation of each line in the graph.
Determine whether the lines are perpendicular.
y
Blue line
Green line











y-intercept is 1
y-intercept is 3

x


These are opposite reciprocals!
The lines are perpendicular!
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Example 1 Write the equation of each line in the
graph. Determine whether the lines are
perpendicular.
y
Blue line
Green line












y-intercept is 4
y-intercept is 3

x

The lines are not perpendicular!
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Example 2 Write the equation of each line in the
graph. Determine whether the lines are
perpendicular.
y
Blue line











Green line
y-intercept is 1
y-intercept is 4

x


The lines are perpendicular!
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Write the slope-intercept form of an equation for
the line that passes through (-4,-3) and is
perpendicular to the graph of 4x y 2.
y
Find the slope of the given line.











Find the opposite reciprocal.
x



Use slope-intercept or point-slope to write the
equation.
(-4,-3)
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Write the slope-intercept form of an equation for
the line that passes through (-4,-3) and is
perpendicular to the graph of 4x y 2.
(when no graph is given)
Find the slope of the given line.
Find the opposite reciprocal.
Use slope-intercept or point-slope to write the
equation.
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Example 3 Write the slope-intercept form of an
equation for the line that passes through (-3,-2)
and is perpendicular to the graph of x 4y 12.

Example 4 Write the slope-intercept form of an
equation for the line that passes through (4,7)
and is perpendicular to the graph of -2x 3y
-3.
Example 5 Write the slope-intercept form of an
equation for the line that passes through (4,-1)
and is perpendicular to the graph of 7x - 2y 3.

Find slope of given line.
Find the opposite reciprocal.
Use slope-intercept or point-slope form to write
the equation.
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Example 3 Write the slope-intercept form of an
equation for the line that passes through (-3,-2)
and is perpendicular to the graph of x 4y 12.

Find slope of given line.
Use slope-intercept or point-slope form to write
the equation.
Find the opposite reciprocal.
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Example 4 Write the slope-intercept form of an
equation for the line that passes through (4,7)
and is perpendicular to the graph of -2x 3y
-3.
Find slope of given line.
Use slope-intercept or point-slope form to write
the equation.
Find the opposite reciprocal.
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Example 5 Write the slope-intercept form of an
equation for the line that passes through (4,-1)
and is perpendicular to the graph of 7x - 2y 3.

Find slope of given line.
Use slope-intercept or point-slope form to write
the equation.
Find the opposite reciprocal.
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Write an equation in slope-intercept form for a
line perpendicular to the graph of -3x 2y 6
that passes through the x-intercept of the line.
(but no graph is given)
y










What is the problem asking you to do?

x
-3x2y6
Write equation for this line.
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Write an equation in slope-intercept form for a
line perpendicular to the graph of -3x 2y 6
that passes through the x-intercept of the line.
Find slope of given line.
Find the x-intercept of the given line.
Coordinate of x-intercept is (-2,0).
Find the opposite reciprocal.
Use slope-intercept or point-slope form to write
the equation.
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Write an equation in slope-intercept form for a
line perpendicular to the graph of -3x 2y 6
that passes through the x-intercept of the line.
y











x
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Example 6 Write an equation in slope-intercept
form for a line perpendicular to the graph of x
3y 6 that passes through the x-intercept of the
line.
Example 7 Write an equation in slope-intercept
form for a line perpendicular to the graph of 3x
2y 8 that passes through the y-intercept of
the line.
Find slope of given line.
Find the opposite reciprocal.
Find the intercept of given line.
Use slope-intercept or point-slope form to write
the equation.
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Example 6 Write an equation in slope-intercept
form for a line perpendicular to the graph of x
3y 6 that passes through the x-intercept of the
line.
Find slope of given line.
Find the x-intercept of the given line.
Coordinate of x-intercept is (6,0).
Use slope-intercept or point-slope form to write
the equation.
Find the opposite reciprocal.
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Example 7 Write an equation in slope-intercept
form for a line perpendicular to the graph of 3x
2y 8 that passes through the y-intercept of
the line.
Find slope of given line.
Find the x-intercept of the given line.
Coordinate of y-intercept is (0,4).
Find the opposite reciprocal.
Use slope-intercept or point-slope form to write
the equation.
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Homework
4-A15 Pages 240-241 1825,28-30,36 and Skills
Practice Wkbk. Page 30 13-24.
Review nightly for trimester 1 exam.