1. concepts, and examples Lesson Objectives: I will be able to …
Identify and graph parallel and perpendicular
lines
Write equations to describe lines parallel or
perpendicular to a given line
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts, and examples

2. Page 29

3. Example 1: Identifying Parallel Lines
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Example 1: Identifying Parallel Lines
Identify which lines are parallel.
The lines described by
and both have slope . These lines are parallel.
The lines described by y = x and y = x + 1 both have slope 1. These lines are parallel.

4. Example 2: Identifying Parallel Lines
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Example 2: Identifying Parallel Lines
Identify which lines are parallel.
Step 1: Write each equation in slope-intercept (y = mx + b) form.
1. y = 2x – 3 2.
3. 2x + 3y = 8
4. y + 1 = 3(x – 3) √
slope = 2
slope = √
slope =
3y = -2x + 8 √
y + 1 = 3x – 9
y = 3x – 10 √
y=2x–3
y+1=3(x–3)
slope = 3
Step 2: Find the slope of each line.
Step 3: Determine whether the lines are parallel.
and 2x + 3y = 8 are parallel because
both have a slope of

5. Identify which lines are parallel.
Your Turn 2
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Identify which lines are parallel.
Step 1: Write each equation in slope-intercept (y = mx + b) form.
slope = 1.
2. -3x + 4y = 32
3. y = 3x
4. y – 1 = 3(x + 2) √
slope =
4y = 3x + 32 √ √
slope = 3 √
slope = 3
y – 1 = 3x + 6
y = 3x + 7
Step 2: Find the slope of each line.
y–1=3(x+2)
–3x+4y=32
y=3x
Step 3: Determine whether the lines are parallel.
y = 3x and y – 1 = 3(x + 2) are parallel because both have a slope of 3.
(Note that and -3x + 4y = 32 are not
parallel; they are the same line!)

6. Example 3: Geometry Application
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Example 3: Geometry Application
Show that JKLM is a parallelogram.
Use the ordered pairs and the slope formula to find the slopes of MJ and KL.
MJ is parallel to KL because they have the same slope.
JK is parallel to ML because they are both horizontal.
Since opposite sides are parallel, JKLM is a parallelogram.

7. AD is parallel to BC because they have the same slope.
Your Turn 3
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Show that the points A(0, 2), B(4, 2), C(1, –3), D(–3, –3) are the vertices of a parallelogram.
Use the ordered pairs and slope formula to find the slopes of AD and BC. •
A(0, 2)
B(4, 2)
D(–3, –3)
C(1, –3)
AD is parallel to BC because they have the same slope.
AB is parallel to DC because they are both horizontal.
Since opposite sides are parallel, ABCD is a parallelogram.

8. Page 30

9. Page 30
Helpful Hint
If you know the slope of a line, the slope of a perpendicular line will be the "opposite reciprocal.”

10. Example 4: Identifying Perpendicular Lines
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Identify which lines are perpendicular:
y = 3; x = –2; y = 3x;
y = 3 is a horizontal line, and x = –2 is a vertical line. These lines are perpendicular.
x = –2
y = 3
The slope of the line described by y = 3x is 3. The slope of the line described by
is .
y =3x
3 and are opposite reciprocals,
so these lines are perpendicular.

11. Your Turn 4 Identify which lines are perpendicular:
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Identify which lines are perpendicular:
y = –4; y – 6 = 5(x + 4); x = 3; y =
x = 3
x = 3 is a vertical line, and y = –4 is a horizontal line. These lines are perpendicular.
The slope of the line described by y – 6 = 5(x + 4) is 5. The slope of the line described by y = is
5 and are opposite reciprocals,
so these lines are perpendicular.
y = –4
y – 6 = 5(x + 4)

12. Example 5: Geometry Application
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Example 5: Geometry Application
Show that ABC is a right triangle.
If ABC is a right triangle, AB will be perpendicular to AC.
slope of
slope of
AB is perpendicular to AC because
Therefore, ABC is a right triangle because it contains a right angle.

13. Example 6: Writing Equations of Parallel and Perpendicular Lines
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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.
Step 2 Write the equation in point-slope form.
y = 3x + 8
The slope is 3.
y – y1 = m(x – x1)
Use the point-slope form.
The parallel line also has a slope of 3.
y – 10 = 3(x – 4)
Step 3 Write the equation in slope-intercept form.
y – 10 = 3(x – 4)
Distribute 3 on the right side.
y – 10 = 3x – 12
Add 10 to both sides.
y = 3x – 2

14. Example 7: Writing Equations of Parallel and Perpendicular Lines
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Example 7: 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.
Step 1 Find the slope of the line.
Step 2 Write the equation in point-slope form.
y = 2x – 5
The slope is 2.
The perpendicular line has a
slope of
y – y1 = m(x – x1)
Step 3 Write the equation in slope-intercept form.

15. Your Turn 7
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Write an equation in slope-intercept form for the line that passes through (–5, 3) and is perpendicular to the line described by y = 5x.
Step 1 Find the slope of the line.
Step 2 Write the equation in point-slope form.
y = 5x
The slope is 5.
y – y1 = m(x – x1)
The perpendicular line has a
slope of
Step 3 Write in slope-intercept form.

16. Chapter 5 Test in two classes!
Homework
Assignment #19.5
Holt 5-8 #9-15 odd, 22-24, 26, 34-36
Chapter 5 Test in two classes!