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Parallel and Perpendicular Lines Exercise, Summaries of Algebra

A worksheet on identifying parallel and perpendicular lines through given equations and points. It includes 15 questions that require identifying slopes, determining if lines are parallel or perpendicular, and writing the equation of a line given its slope and a point it passes through.

Typology: Summaries

2021/2022

Uploaded on 09/12/2022

oliver97
oliver97 ๐Ÿ‡บ๐Ÿ‡ธ

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Parallel and Perpendicular Lines
Name________________________________________________________________ Date__________________
Fill in the blank or write the answer to the question.
1. A line that is parallel to y = 3
4๐‘ฅ โˆ’ 9 has slope m = ______
2. A line that is perpendicular to 3y = 11 โ€“ 8x has slope m =________
3. A line that is parallel to y = 12 has slope m = __________
4. Are the lines 2y โ€“ x = 6 and 6x โ€“ 3y โ€“ 33 = 0 parallel, perpendicular, or neither? ________________
Choose the best answer.
5. Which equation represents a line that is
perpendicular to the line shown below?
A. y = 2
3๐‘ฅ + 5
B. y = 3
2๐‘ฅ โˆ’ 4
C. y = โˆ’2
3๐‘ฅ โˆ’ 6
D. y = โˆ’3
2๐‘ฅ + 1
6. Which equation represents a line that is
parallel to the line shown below?
A. y = 3
5๐‘ฅ + 1
B. y = โˆ’3
5๐‘ฅ + 1
C. y = 5
3๐‘ฅ โˆ’ 1
D. y = โˆ’5
3๐‘ฅ โˆ’ 1
7. Which describes the lines y = 7
8๐‘ฅ + 12
and y = โˆ’8
7๐‘ฅ + 7?
A. Parallel
B. Perpendicular
C. Neither
8. Which describes the lines x โ€“ 2y = โ€“ 6
and 4y + 4 = 2x?
A. Parallel
B. Perpendicular
C. Neither
9. Which describes the lines shown below?
A. Parallel
B. Perpendicular
C. Neither
10. Which describes the lines shown below?
A. Parallel
B. Perpendicular
C. Neither
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Parallel and Perpendicular Lines

Name________________________________________________________________ Date__________________

Fill in the blank or write the answer to the question.

  1. A line that is parallel to y = 34 ๐‘ฅ โˆ’ 9 has slope m = ______
  2. A line that is perpendicular to 3y = 11 โ€“ 8x has slope m =________
  3. A line that is parallel to y = 12 has slope m = __________
  4. Are the lines 2y โ€“ x = 6 and 6x โ€“ 3y โ€“ 33 = 0 parallel, perpendicular, or neither? ________________

Choose the best answer.

  1. Which equation represents a line that is perpendicular to the line shown below? A. y = 23 ๐‘ฅ + 5 B. y = 32 ๐‘ฅ โˆ’ 4 C. y = โˆ’ 23 ๐‘ฅ โˆ’ 6 D. y = โˆ’ 32 ๐‘ฅ + 1
  2. Which equation represents a line that is parallel to the line shown below? A. y = 35 ๐‘ฅ + 1 B. y = โˆ’ 35 ๐‘ฅ + 1 C. y = 53 ๐‘ฅ โˆ’ 1 D. y = โˆ’ 53 ๐‘ฅ โˆ’ 1
  3. Which describes the lines y = 78 ๐‘ฅ + 12 and y = โˆ’ 87 ๐‘ฅ + 7?

A. Parallel B. Perpendicular C. Neither

  1. Which describes the lines x โ€“ 2y = โ€“ 6 and 4y + 4 = 2x?

A. Parallel B. Perpendicular C. Neither

  1. Which describes the lines shown below? A. Parallel B. Perpendicular C. Neither
  2. Which describes the lines shown below?

A. Parallel B. Perpendicular C. Neither

Write the equation of the line that is described. Give your answer in slope intercept form.

  1. A line that is parallel to the one shown below that passes through the point (8, โ€“ 7).

___________________________________

  1. A line that is perpendicular to the one shown below that passes through the point (12,3).

_______________________________________

  1. A line that is parallel to 3y = x +12 and that passes through the point (6, โ€“ 8).

_______________________________________

  1. A line that is perpendicular to y โ€“ x = 7 and passes through the point (โ€“2, โ€“ 2).

________________________________________

  1. Lines s, t, and u all lie on the same plane. Line s is parallel to line t. Line t is perpendicular to line u. What is the relationship between lines s and u? How do you know?