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5-8 Slopes of Parallel and Perpendicular Lines5-8Slopes of Parallel and
Perpendicular Lines
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Holt Algebra 1Holt Algebra 1
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Lesson QuizLesson Quiz
5-8 Slopes of Parallel and Perpendicular Lines
Bell Quiz 5-8
Find the reciprocal.
1. 2 2.
3.
1 pt 1 pt
1 pt
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Find the slope of the line that passes througheach pair of points.
4. (2, 2) and (–1, 3)
5. (3, 4) and (4, 6)
6. (5, 1) and (0, 0)
10 pts
possible
1 pt
2 pts
2 pts
2 pts
1 pt for putting your name on your paper
5-8 Slopes of Parallel and Perpendicular Lines
Questions on 5-7
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5-8 Slopes of Parallel and Perpendicular Lines
Questions on 5-7
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
Objectives
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Write equations to describe lines parallel or perpendicular to a given line.
5-8 Slopes of Parallel and Perpendicular Lines
Vocabulary
parallel lines
perpendicular lines
Holt Algebra 1
5-8 Slopes of Parallel and Perpendicular Lines
To sell at a particular farmers’ market for a year, there is a $100 membership fee. Then you pay $3 for each hour that you sell at the market. However, if you were a member the previous year, the membership fee is reduced to $50.
• The red line shows the
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• The red line shows the total cost if you are a new member.
• The blue line shows the total cost if you are a returning member.
5-8 Slopes of Parallel and Perpendicular Lines
These two lines are parallel. Parallel lines are lines in the same plane that have no points in common. In other words, they do not
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other words, they do not intersect.
5-8 Slopes of Parallel and Perpendicular Lines
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5-8 Slopes of Parallel and Perpendicular Lines
Example 1A: Identifying Parallel Lines
Identify which lines are parallel.
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5-8 Slopes of Parallel and Perpendicular Lines
Example 1B: Identifying Parallel Lines
Identify which lines are parallel.
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5-8 Slopes of Parallel and Perpendicular Lines
Example 1B Continued
The lines described by y = 2x – 3and y + 1 = 3(x – 3) are not parallel with any of the lines.
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y = 2x – 3
y + 1 = 3(x – 3)
The lines described by
and
represent parallel lines. They
each have the slope .
5-8 Slopes of Parallel and Perpendicular Lines
Check It Out! Example 1a
y = 2x + 2
Identify which lines are parallel.
y = 2x + 2; y = 2x + 1; y = –4; x = 1
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y = 2x + 1
y = 2x + 2
y = –4
x = 1
5-8 Slopes of Parallel and Perpendicular Lines
Check It Out! Example 1b
Identify which lines are parallel.
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5-8 Slopes of Parallel and Perpendicular Lines
Check It Out! Example 1b Continued
The lines described by
–3x + 4y = 32 and y = + 8
have the same slope, but they
–3x + 4y = 32
y = 3x
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are not parallel lines. They are
the same line.
y – 1 = 3(x + 2)
The lines described by
y = 3x and y – 1 = 3(x + 2)represent parallel lines. They each have slope 3.
5-8 Slopes of Parallel and Perpendicular Lines
Example 2: Geometry Application
Show that JKLM is a parallelogram.
Use the ordered pairs and the slope
formula to find the slopes of MJ and KL.
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5-8 Slopes of Parallel and Perpendicular Lines
Check It Out! Example 2
Show that the points A(0, 2), B(4, 2), C(1, –3), D(–3, –3) are the vertices of a parallelogram.
••A(0, 2) B(4, 2)
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• •
••
D(–3, –3) C(1, –3)
5-8 Slopes of Parallel and Perpendicular Lines
Perpendicular lines are lines that intersect to form right angles (90°).
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5-8 Slopes of Parallel and Perpendicular Lines
Helpful Hint
If you know the slope of a line, the slope of a perpendicular line will be the "opposite reciprocal.”
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5-8 Slopes of Parallel and Perpendicular Lines
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5-8 Slopes of Parallel and Perpendicular Lines
Identify which lines are perpendicular: y = 3;
x = –2; y = 3x; .
y = 3x = –2
Example 3: Identifying Perpendicular Lines
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y =3x
5-8 Slopes of Parallel and Perpendicular Lines
Identify which lines are perpendicular: y = 3;
x = –2; y = 3x; .
y = 3x = –2
Example 3 Continued
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y =3x
5-8 Slopes of Parallel and Perpendicular Lines
Check It Out! Example 3
Identify which lines are perpendicular: y = –4;
y – 6 = 5(x + 4); x = 3; y =
x = 3
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y = –4
y – 6 = 5(x + 4)
5-8 Slopes of Parallel and Perpendicular Lines
Check It Out! Example 3 Continued
Identify which lines are perpendicular: y = –4;
y – 6 = 5(x + 4); x = 3; y =
x = 3
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y = –4
y – 6 = 5(x + 4)
5-8 Slopes of Parallel and Perpendicular Lines
Example 4A: Writing Equations of Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8.
Step 1 Find the slope of the line.
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Step 2 Write the equation in point-slope form.
Step 3 Write the equation in slope-intercept form
5-8 Slopes of Parallel and Perpendicular Lines
Example 4B: Writing Equations of Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that passes through (2, –1) and is perpendicular to the line described by y = 2x – 5.
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5-8 Slopes of Parallel and Perpendicular Lines
Check It Out! Example 4a
Write an equation in slope-intercept form for
the line that passes through (5, 7) and is
parallel to the line described by y = x – 6.
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5-8 Slopes of Parallel and Perpendicular Lines
Check It Out! Example 4bWrite an equation in slope-intercept form for
the line that passes through (–5, 3) and is
perpendicular to the line described by y = 5x.
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5-8 Slopes of Parallel and Perpendicular Lines
• Sec 5-8 (Pg 353) 1-8, 9, 12,
15, 17, 18, 20, 22, 25, 28, 31,
34, 37, 40, 43, 60, 61, 63, 64
HOMEWORK
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34, 37, 40, 43, 60, 61, 63, 64
