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
13. (0, 2) , y = −5x + 8
ANSWER: y = −5x + 2
15. (−2, 3) ,
ANSWER: 17. GEOMETRY A trapezoid is a quadrilateral that has exactly one pair of parallel opposite sides. Is ABCD a trapezoid? Explain.
ANSWER: and the line containing
Yes; the line containing
parallel. The slope of
is undefined and the slope of
19. Determine whether the graphs of y = −6x + 4 and y =
have the same slope, . Therefore one pair of sides is
is .
are perpendicular. Explain.
ANSWER: Yes; the slopes are −6 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
ANSWER: 2x − 8y = −24 and 4x + y = −2 are perpendicular; 2x − 8y = −24 and x − 4y = 4 are parallel.
Write
an equation
slope-intercept
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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
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21. 2x − 8y = −24, 4x + y = −2, x − 4y = 4
ANSWER: 4-4 Parallel
2x − 8y =and
and 4x + y = −2Lines
are perpendicular; 2x − 8y = −24 and x − 4y = 4 are parallel.
−24Perpendicular
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: 25. (−4, 5),
ANSWER: y = −3x − 7
27. (3, 8), y = 5x − 3
ANSWER: Write an equation in slope-intercept form for a line perpendicular to the graph of the equation that passes
through the x-intercept of that line.
29. ANSWER: y = 2x + 16
31. y = 5x + 3
ANSWER: Determine whether the graphs of each pair of equations are parallel , perpendicular , or neither.
33. y = 4x + 3
4x + y = 3
ANSWER: neither
35. 3x + 5y = 10
5x − 3y = −6
ANSWER: perpendicular
37. 2x + 5y = 15
3x + 5y = 15
ANSWER: neither
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39. Write an equation of the line that is parallel to the graph of y = 7x − 3 and passes through the origin.
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35. 3x + 5y = 10
5x − 3y = −6
ANSWER: 4-4 Parallel
and Perpendicular Lines
perpendicular
37. 2x + 5y = 15
3x + 5y = 15
ANSWER: neither
39. Write an equation of the line that is parallel to the graph of y = 7x − 3 and passes through the origin.
ANSWER: y = 7x
41. ARCHAEOLOGY In the ruins of an ancient civilization, an archaeologist found pottery at (2, 6) and hair
accessories at (4, −1). A pole is found with one end at (7, 10) and the other end at (14, 12). Is the pole perpendicular
to the line through the pottery and the hair accessories? Explain.
ANSWER: Yes; the slope of the line through the hair accessories and the pottery is
endpoints of the pole is
. The slope of the line through the
, so the lines are perpendicular.
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