Worksheet: Equations of Parallel and Perpendicular Lines

In this worksheet, we will practice writing the equation of a line parallel or perpendicular to another line.

Q1:

Write, in the form 𝑦 = 𝑚 𝑥 + 𝑐 , the equation of the line through ( 1 , 1 ) that is parallel to the line 6 𝑥 𝑦 + 4 = 0 .

  • A 𝑦 = 6 𝑥 5
  • B 𝑦 = 6 𝑥 + 5
  • C 𝑦 = 1 6 𝑥 + 7
  • D 𝑦 = 6 𝑥 7

Q2:

Find, in slope-intercept form, the equation of the line parallel to 𝑦 = 8 3 𝑥 + 3 that passes through point 𝐴 ( 3 , 2 ) .

  • A 𝑦 = 3 8 𝑥 + 2 5 8
  • B 𝑦 = 8 3 𝑥 + 6
  • C 𝑦 = 3 8 𝑥 2 5 8
  • D 𝑦 = 8 3 𝑥 6
  • E 𝑦 = 6 𝑥 + 8 3

Q3:

A straight line 𝐿 has the equation 𝑦 = 2 𝑥 3 . Find the equation of the line parallel to 𝐿 that passes through the point ( 1 , 3 ) .

  • A 𝑦 = 1 2 𝑥 + 5 2
  • B 𝑦 = 2 𝑥 1
  • C 𝑦 = 1 2 𝑥 + 7 2
  • D 𝑦 = 2 𝑥 + 5
  • E 𝑦 = 2 𝑥 + 7

Q4:

Write, in the form 𝑦 = 𝑚 𝑥 + 𝑐 , the equation of the line through ( 1 , 2 ) that is parallel to the line 3 𝑥 3 𝑦 + 7 = 0 .

  • A 𝑦 = 𝑥 5 3
  • B 𝑦 = 𝑥 + 3
  • C 𝑦 = 𝑥 + 1 3
  • D 𝑦 = 𝑥 + 1

Q5:

Write, in the form 𝑦 = 𝑚 𝑥 + 𝑐 , the equation of the line through ( 2 , 3 ) that is parallel to the line 3 𝑥 𝑦 + 9 = 0 .

  • A 𝑦 = 3 𝑥 9
  • B 𝑦 = 3 𝑥 + 9
  • C 𝑦 = 1 3 𝑥 + 3
  • D 𝑦 = 3 𝑥 3

Q6:

Find, in slope-intercept form, the equation of the line parallel to 𝑦 = 9 1 0 𝑥 + 4 that passes through point 𝐴 ( 1 , 5 ) .

  • A 𝑦 = 1 0 9 𝑥 + 5 5 9
  • B 𝑦 = 9 1 0 𝑥 4 1 1 0
  • C 𝑦 = 1 0 9 𝑥 5 5 9
  • D 𝑦 = 9 1 0 𝑥 + 4 1 1 0
  • E 𝑦 = 4 1 1 0 𝑥 9 1 0

Q7:

Find, in slope-intercept form, the equation of the line parallel to 𝑦 = 1 8 𝑥 + 4 that passes through point 𝐴 ( 1 , 5 ) .

  • A 𝑦 = 8 𝑥 + 1 3
  • B 𝑦 = 1 8 𝑥 3 9 8
  • C 𝑦 = 8 𝑥 1 3
  • D 𝑦 = 1 8 𝑥 + 3 9 8
  • E 𝑦 = 3 9 8 𝑥 + 1 8

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