4-4 Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that passes through the given point and is parallel
to the graph of given equation.
11. (3, −2) , y = x + 4
ANSWER: y=x−5
12. (4, −3) , y = 3x − 5
ANSWER: y = 3x − 15
13. (0, 2) , y = −5x + 8
ANSWER: y = −5x + 2
14. (−4, 2) ,
ANSWER: 15. (−2, 3) ,
ANSWER: 16. (9, 12) , y = 13x − 4
ANSWER: 19. Determine whether the graphs of y = −6x + 4 and y =
are perpendicular. Explain.
ANSWER: Yes; the slopes are −6 and
.
20. MAPS On a map, Elmwood Drive passes through R(4, −11) and S(0, −9), and Taylor Road passes through J(6, −2)
and K(4, −5). If they are straight lines, are the two streets perpendicular? Explain.
ANSWER: No; the slopes are
and .
CCSS PERSEVERANCE Determine whether the graphs of the following equations are parallel or
perpendicula r. Explain.
21. 2x − 8y = −24, 4x + y = −2, x − 4y = 4
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ANSWER: 2x − 8y = −24 and x − 4y = 4 are perpendicular to 4x + y = −2; 2x − 8y = −24 and x − 4y = 4 are parallel.
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and K(4, −5). If they are straight lines, are the two streets perpendicular? Explain.
ANSWER: 4-4 Parallel
and Perpendicular
No; the slopes
are
.
and Lines
CCSS PERSEVERANCE Determine whether the graphs of the following equations are parallel or
perpendicula r. Explain.
21. 2x − 8y = −24, 4x + y = −2, x − 4y = 4
ANSWER: 2x − 8y = −24 and x − 4y = 4 are perpendicular to 4x + y = −2; 2x − 8y = −24 and x − 4y = 4 are parallel.
22. 3x − 9y = 9, 3y = x + 12, 2x − 6y = 12
ANSWER: All of the lines are parallel.
Write an equation in slope-intercept form for the line that passes through the given point and is
perpendicular to the graph of the equation.
23. (−3, −2), y = −2x + 4
ANSWER: 24. (-5, 2),
ANSWER: y = −2x − 8
25. (−4, 5),
ANSWER: y = −3x − 7
26. (2, 6),
ANSWER: y = 4x − 2
27. (3, 8), y = 5x − 3
ANSWER: 28. (4, −2), y = 3x + 5
ANSWER: Determine whether the graphs of each pair of equations are parallel , perpendicular , or neither.
33. y = 4x + 3
4x + y = 3
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ANSWER: neither
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28. (4, −2), y = 3x + 5
ANSWER: 4-4 Parallel and Perpendicular Lines
Determine whether the graphs of each pair of equations are parallel , perpendicular , or neither.
33. y = 4x + 3
4x + y = 3
ANSWER: neither
34. y = −2x
2x + y = 3
ANSWER: parallel
35. 3x + 5y = 10
5x − 3y = −6
ANSWER: perpendicular
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