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Lesson: Equations of Parallel and Perpendicular Lines

Sample Question Videos

Worksheet • 7 Questions • 3 Videos

Q1:

Write, in the form 𝑦 = π‘š π‘₯ + 𝑐 , the equation of the line through ( βˆ’ 1 , βˆ’ 1 ) that is parallel to the line βˆ’ 6 π‘₯ βˆ’ 𝑦 + 4 = 0 .

  • A 𝑦 = βˆ’ 6 π‘₯ βˆ’ 7
  • B 𝑦 = 6 π‘₯ + 5
  • C 𝑦 = βˆ’ 1 6 π‘₯ + 7
  • D 𝑦 = βˆ’ 6 π‘₯ βˆ’ 5

Q2:

Write, in the form 𝑦 = π‘š π‘₯ + 𝑐 , the equation of the line through ( 1 , 2 ) that is parallel to the line 3 π‘₯ βˆ’ 3 𝑦 + 7 = 0 .

  • A 𝑦 = π‘₯ + 1
  • B 𝑦 = βˆ’ π‘₯ + 3
  • C 𝑦 = π‘₯ + 1 3
  • D 𝑦 = π‘₯ βˆ’ 5 3

Q3:

Write, in the form 𝑦 = π‘š π‘₯ + 𝑐 , the equation of the line through ( βˆ’ 2 , 3 ) that is parallel to the line βˆ’ 3 π‘₯ βˆ’ 𝑦 + 9 = 0 .

  • A 𝑦 = βˆ’ 3 π‘₯ βˆ’ 3
  • B 𝑦 = 3 π‘₯ + 9
  • C 𝑦 = βˆ’ 1 3 π‘₯ + 3
  • D 𝑦 = βˆ’ 3 π‘₯ βˆ’ 9

Q4:

Find, in slope-intercept form, the equation of the line parallel to 𝑦 = βˆ’ 8 3 π‘₯ + 3 that passes through point 𝐴 ( βˆ’ 3 , 2 ) .

  • A 𝑦 = βˆ’ 8 3 π‘₯ βˆ’ 6
  • B 𝑦 = βˆ’ 6 π‘₯ + 8 3
  • C 𝑦 = βˆ’ 8 3 π‘₯ + 6
  • D 𝑦 = 3 8 π‘₯ βˆ’ 2 5 8
  • E 𝑦 = 3 8 π‘₯ + 2 5 8

Q5:

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

  • A 𝑦 = 9 1 0 π‘₯ + 4 1 1 0
  • B 𝑦 = 4 1 1 0 π‘₯ βˆ’ 9 1 0
  • C 𝑦 = 9 1 0 π‘₯ βˆ’ 4 1 1 0
  • D 𝑦 = βˆ’ 1 0 9 π‘₯ βˆ’ 5 5 9
  • E 𝑦 = βˆ’ 1 0 9 π‘₯ + 5 5 9

Q6:

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

  • A 𝑦 = βˆ’ 1 8 π‘₯ + 3 9 8
  • B 𝑦 = 3 9 8 π‘₯ + 1 8
  • C 𝑦 = βˆ’ 1 8 π‘₯ βˆ’ 3 9 8
  • D 𝑦 = 8 π‘₯ βˆ’ 1 3
  • E 𝑦 = 8 π‘₯ + 1 3

Q7:

A straight line 𝐿 has the equation 𝑦 = βˆ’ 2 π‘₯ βˆ’ 3 . Find the equation of the line parallel to 𝐿 that passes through the point ( 1 , 3 ) .

  • A 𝑦 = βˆ’ 2 π‘₯ + 5
  • B 𝑦 = βˆ’ 2 π‘₯ + 7
  • C 𝑦 = 2 π‘₯ βˆ’ 1
  • D 𝑦 = βˆ’ 1 2 π‘₯ + 7 2
  • E 𝑦 = 1 2 π‘₯ + 5 2
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