Warm Up

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Warm Up Find the value of m. 1. 2. 3.
4.
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Objectives
Find the slope of a line. Use slopes to identify
parallel and perpendicular lines.
Vocabulary
rise run slope
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The slope of a line in a coordinate plane is a
number that describes the steepness of the line.
Any two points on a line can be used to determine
the slope.
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Example 1A Finding the Slope of a Line
Use the slope formula to determine the slope of
each line.
Substitute (2, 7) for (x1, y1) and (3, 7) for
(x2, y2) in the slope formula and then simplify.
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Example 1B Finding the Slope of a Line
Use the slope formula to determine the slope of
each line.
Substitute (2, 7) for (x1, y1) and (4, 2) for
(x2, y2) in the slope formula and then simplify.
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Example 1C Finding the Slope of a Line
Use the slope formula to determine the slope of
each line.
Substitute (2, 7) for (x1, y1) and (2, 1) for
(x2, y2) in the slope formula and then simplify.
The slope is undefined.
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Example 1D Finding the Slope of a Line
Use the slope formula to determine the slope of
each line.
Substitute (4, 2) for (x1, y1) and (2, 1) for
(x2, y2) in the slope formula and then simplify.
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Check It Out! Example 1
Substitute (3, 1) for (x1, y1) and (2, 1) for
(x2, y2) in the slope formula and then simplify.
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One interpretation of slope is a rate of change.
If y represents miles traveled and x represents
time in hours, the slope gives the rate of change
in miles per hour.
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Example 2 Transportation Application
Justin is driving from home to his college
dormitory. At 400 p.m., he is 260 miles from
home. At 700 p.m., he is 455 miles from home.
Graph the line that represents Justins distance
from home at a given time. Find and interpret the
slope of the line.
Use the points (4, 260) and (7, 455) to graph the
line and find the slope.
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Example 2 Continued
The slope is 65, which means Justin is traveling
at an average of 65 miles per hour.
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Check It Out! Example 2
What if? Use the graph below to estimate how far
Tony will have traveled by 630 P.M. if his
average speed stays the same.
Since Tony is traveling at an average speed of 60
miles per hour, by 630 P.M. Tony would have
traveled 390 miles.
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Example 3A Determining Whether Lines Are
Parallel, Perpendicular, or Neither
Graph each pair of lines. Use their slopes to
determine whether they are parallel,
perpendicular, or neither.
The products of the slopes is 1, so the lines
are perpendicular.
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Example 3B Determining Whether Lines Are
Parallel, Perpendicular, or Neither
Graph each pair of lines. Use their slopes to
determine whether they are parallel,
perpendicular, or neither.
The slopes are not the same, so the lines are not
parallel. The product of the slopes is not 1, so
the lines are not perpendicular.
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Example 3C Determining Whether Lines Are
Parallel, Perpendicular, or Neither
Graph each pair of lines. Use their slopes to
determine whether they are parallel,
perpendicular, or neither.
The lines have the same slope, so they are
parallel.
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Check It Out! Example 3a
Graph each pair of lines. Use slopes to determine
whether the lines are parallel, perpendicular, or
neither.
Vertical and horizontal lines are perpendicular.
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Check It Out! Example 3b
Graph each pair of lines. Use slopes to determine
whether the lines are parallel, perpendicular, or
neither.
KL and MN for K(4, 4), L(2, 3), M(3, 1), and
N(5, 1)
The slopes are not the same, so the lines are not
parallel. The product of the slopes is not 1, so
the lines are not perpendicular.
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Check It Out! Example 3c
Graph each pair of lines. Use slopes to determine
whether the lines are parallel, perpendicular, or
neither.
The lines have the same slope, so they are
parallel.
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Lesson Quiz
1. Use the slope formula to determine the slope
of the line that passes through M(3, 7) and N(3,
1).
m 1
Graph each pair of lines. Use slopes to determine
whether they are parallel, perpendicular, or
neither.
4, 4 parallel