Name _________________________________________ Date_______________ Class hour _______
Parallel and Perpendicular Lines Independent Practice
1. Indicate whether the lines are parallel, perpendicular, or neither. Justify your answer.
a. 𝑦 = 4𝑥 − 1 and 12𝑥 = 3𝑦 + 7
b. 𝑥 − 7𝑦 = 10 and 2𝑥 + 14𝑦 = 21
c. 5𝑥 + 6𝑦 = 18 and 18𝑥 − 15𝑦 = 36
d. 𝑥 = −1 and 𝑦 = −1
2. Consider the graph below.
𝑛
Part A: Name a set of lines that are parallel.
Justify your answer.
𝑟
𝑚
𝑝
Part B: Name a set of lines that are
perpendicular? Justify your answer.
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3. Match each of the following with the equations below. Write the letter of the appropriate
equation in the column beside each item.
A. 𝑦 = 0
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B. 𝑦 = − 3 𝑥 + 1
C. 𝑥 = 3𝑦 + 21
D. 𝑥 − 2𝑦 = −2
1
A line parallel to 𝑦 = 3 𝑥 + 2
A line perpendicular to 𝑥 = 3
A line perpendicular to 9𝑥 − 3𝑦 = 18
A line parallel to −4𝑥 + 8𝑦 = 9
4. Write the equation of the line that it is parallel to 𝟐𝒙 = 𝟏 − 𝟑𝒚 and passes through(𝟗, 𝟒).
5. Write the equation of the line that it is perpendicular to 𝟓𝒙 + 𝟖𝒚 = 𝟏𝟔 and passes
through(−𝟓, 𝟕).
6. Write the equation of the line that it is perpendicular to 𝒚 = 𝟕𝒙 − 𝟑 and passes through the
origin.
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7. The equation for line 𝐴 is given by 𝑦 = 3 𝑥 + 4. Suppose line 𝐴 is parallel to line 𝐵 and line 𝑇
is perpendicular to line 𝐴. Point (−3, 1) lies on both line 𝐵 and line 𝑇.
Part A: Write an equation for line 𝐵.
Part B: Write an equation for line 𝑇.
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