Name ——————————————————————— Date ————————————

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ed.Write an equation of a perpendicular line

Write an equation of the line that passes through (22, 1) and is

perpendicular to the line y 5 2 1 } 3 x 1 2.

Solution

SteP 1 Identify the slope. The graph of the given equation has a slope of 2 1 } 3 .

Because the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line through (22, 1) is 3.

SteP 2 Find the y-intercept. Use the slope and the given point in y 5 mx 1 b.

1 5 3(22) 1 b Substitute 3 for m, 22 for x, and 1 for y.

7 5 b Solve for b.

SteP 3 Write the equation. Use y 5 mx 1 b.

y 5 3x 1 7 Substitute 3 for m and 7 for b.

exercises for examples 2 and 3 3. Determine which of the following lines, if any, are parallel or perpendicular.

Line a: 23x 2 12y 5 36 Line b: x 1 4y 5 2 Line c: y 5 4x

4. Write an equation of the line that passes through (5, 3) and is perpendicular to the line y 5 25x 1 3.

examPLe 3

Determine whether lines are parallel or perpendicular

Determine which of the following lines, if any, are parallel or

perpendicular: Line a: 4y 2 6y 5 28, Line b: y 5 2 2 } 3 x 1 1,

Line c: 2x 1 3y 5 215.

Solution

Find the slopes of the lines.

Line b: The equation is in slope-intercept form. The slope is 2 2 } 3 .

Write the equations for lines a and c in slope-intercept form.

Line a: 4y 2 6x 5 28 Line c: 2x 1 3y 5 215

4y 5 6x 2 8 3y 5 22x 2 15

y 5 3 }

2 x 2 2 y 5 2

2 }

3 x 2 5

Lines b and c have a slope of 2 2 }

3 , so they are parallel. Line a has a slope of

3 }

2 , the

negative reciprocal of 2 2 }

3 , so it is perpendicular to lines b and c.

examPLe 2

Study guide continuedFor use with the lesson “Write Equations of Parallel and Perpendicular Lines”

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Algebra 1Chapter Resource Book4-56

Lesson

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Lesson Write Equations of Parallel and Perpendicular Lines, continued

Practice Level B

1. y 5 5x 2 13 2. y 5 2 }

3 x 2 4

3. y 5 24x 2 23 4. y 5 6x 1 25

5. y 5 22x 28 6. y 5 1 }

2 x 1

31 }

2

7. y 5 2 1 } 3 x 2

2 }

3 8. y 5 2

3 } 2 x 1

15 }

2

9. y 5 5x 2 22 10. y 5 2 1 } 2 x 2

5 }

2

11. y 5 2 5 } 2 x 1 14 12. y 5

3 }

8 x 2

13 }

2

13. Lines b and c are perpendicular. 14. Lines a and b and lines b and c are perpendicular. Lines a and c are parallel. 15. Lines a and b and lines b and c are perpendicular. Lines a and c are parallel.

16. a. y 5 2 }

3 x 1 4 b. y 5 2

4 } 3 x 1 4 c. No. The

lines for part A and part B are not perpendicular.

17. a. you: y 5 1 }

2 x; your friend: y 5

1 }

2 x 1 5

b. you: 10 sandwiches; your friend: 15 sandwiches c. The graphs are parallel because they have the same slope but different y-intercepts.

Practice Level C

1. y 5 24x 2. y 5 x 2 13

3. y 5 7 }

3 x 1 4 4. y 5

6 } 5 x 1

73 } 5

5. y 5 2 8 } 3 x 1

25 }

3 6. y 5 2

2 } 9 x 1

4 }

3

7. y 5 2 2 } 3 x 1

25 }

3 8. y 5 2

3 } 4 x 1

7 }

4

9. y 5 1 }

4 x 2 3 10. y 5 2

6 } 5 x 2

63 } 5

11. y 5 8 }

9 x 2 8 12. y 5 2

2 } 3 x 1

62 }

3

13. none 14. Lines a and b are perpendicular.

15. Lines a and b are perpendicular.

16. y 5 0.8x 1 11.15; The slope of the line that

represents Main Street is 2 5 } 4 , so the line that

represents Wooster Street must be 4 } 5 in order to

be perpendicular to the line that represents Main Street.

17. a. y 5 20 1 7x b. y 5 32 1 7x c. The graphs are parallel because they have the same slope but different y-intercepts. d. $12; $12; $12

Study Guide

1. y 5 2 }

3 x 2 4 2. y 5 22x 2 10

3. a i b, a ⊥ c, b ⊥ c 4. y 5 1 } 5 x 1 2

Problem Solving Workshop: Worked Out Example

1. y 5 1 }

2 x 1 7 2. y 5 22x 1 17

3. The slope should be the negative reciprocal

of 22, which is 1 }

2 . The equation of June Road

is y 5 1 }

2 x 1 7.

Challenge Practice

1. 1 }

3 2 y 2.

x 2 1 }

3 2 y 3. 0 4.

x 2 a }

b 2 y

5. y 2 q 5 d 2 b

} c 2 a

(x 2 p), c Þ a

6. y 2 q 5 2(x 2 p), b Þ a 7. y 2 b 5 x, b Þ a

8. y 5 x 1 b, b Þ a

9. y 2 q 5 c 2 a

} b 2 d

(x 2 p), b Þ d

10. y 2 q 5 x 2 p, b Þ a

11. y 2 b 5 2x, b Þ a 12. y 5 x 1 b, b Þ a

Lesson Fit a Line to Data

Teaching Guide

1.

x

y

1

1

5

3

7

1 3 5 7 9

2. As x increases, y tends to increase.

3.

x

y

5

7

1 3 5 7 9

y 5 3

y 5 2x 2 4

y 5 x 1 12 3

y 5 2 x 1 91 2

Algebra 1Chapter Resource BookA46

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