Worksheet: Equation of a Perpendicular Line

In this worksheet, we will practice writing the equation of a line perpendicular to a given line if we know a point on the line and the equation of the given line.

Q1:

Find, in slope-intercept form, the equation of the line perpendicular to 𝑦 = 2 𝑥 4 that passes through the point 𝐴 ( 3 , 3 ) .

  • A 𝑦 = 2 𝑥 9
  • B 𝑦 = 1 2 𝑥 + 3 2
  • C 𝑦 = 2 𝑥 + 9
  • D 𝑦 = 1 2 𝑥 3 2
  • E 𝑦 = 3 2 𝑥 + 1 2

Q2:

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

  • A 𝑦 = 2 𝑥 + 9
  • B 𝑦 = 1 2 𝑥 3 2
  • C 𝑦 = 2 𝑥 9
  • D 𝑦 = 1 2 𝑥 + 3 2
  • E 𝑦 = 3 2 𝑥 1 2

Q3:

Find, in slope-intercept form, the equation of the line perpendicular to 𝑦 = 2 𝑥 + 2 that passes through the point 𝐴 ( 5 , 1 ) .

  • A 𝑦 = 2 𝑥 + 1 1
  • B 𝑦 = 1 2 𝑥 + 3 2
  • C 𝑦 = 2 𝑥 1 1
  • D 𝑦 = 1 2 𝑥 3 2
  • E 𝑦 = 3 2 𝑥 + 1 2

Q4:

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

  • A 𝑦 = 9 𝑥 + 1 3
  • B 𝑦 = 1 9 𝑥 3 5 9
  • C 𝑦 = 9 𝑥 1 3
  • D 𝑦 = 1 9 𝑥 + 3 5 9
  • E 𝑦 = 3 5 9 𝑥 + 1 9

Q5:

Find, in slope-intercept form, the equation of the line perpendicular to 𝑦 = 4 𝑥 + 2 that passes through the point 𝐴 ( 3 , 3 ) .

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

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