Lesson Worksheet: Equations of Parallel and Perpendicular Lines Mathematics

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

Q1:

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

  • A𝑦=−6𝑥−7
  • B𝑦=−6𝑥−5
  • C𝑦=6𝑥+5
  • D𝑦=−16𝑥+7

Q2:

Find, in slope-intercept form, the equation of the line parallel to 𝑦=−83𝑥+3 that passes through point 𝐴(−3,2).

  • A𝑦=38𝑥+258
  • B𝑦=38𝑥−258
  • C𝑦=−6𝑥+83
  • D𝑦=−83𝑥+6
  • E𝑦=−83𝑥−6

Q3:

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

  • A𝑦=12𝑥+52
  • B𝑦=−2𝑥+5
  • C𝑦=−2𝑥+7
  • D𝑦=2𝑥−1
  • E𝑦=−12𝑥+72

Q4:

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

  • A𝑦=−12𝑥−32
  • B𝑦=2𝑥−9
  • C𝑦=−12𝑥+32
  • D𝑦=−32𝑥+12
  • E𝑦=2𝑥+9

Q5:

Determine, in slope-intercept form, the equation of the line passing through 𝐴(13,−7) perpendicular to the line passing through 𝐵(8,−9) and 𝐶(−8,10).

  • A𝑦=−1916𝑥+13516
  • B𝑦=1619𝑥+34119
  • C𝑦=−34119𝑥+1619
  • D𝑦=−1916𝑥−13516
  • E𝑦=1619𝑥−34119

Q6:

Write, in the form 𝑦=𝑚𝑥+𝑐, the equation of the line that is parallel to the line −4𝑥+7𝑦−4=0 and that intercepts the 𝑦-axis at 1.

  • A𝑦=𝑥−4
  • B𝑦=−74𝑥+1
  • C𝑦=−4𝑥+1
  • D𝑦=47𝑥
  • E𝑦=47𝑥+1

Q7:

Consider the triangle on 𝐴(−6,9), 𝐵(4,−3), and 𝐶(1,−6), and let 𝐷 be the midpoint of 𝐴𝐵. Now let 𝐸 on 𝐴𝐶 be the intersection of the parallel to ⃖⃗𝐵𝐶 through the point 𝐷. Find the equation of ⃖⃗𝐷𝐸 in the form 𝑦=𝑚𝑥+𝑐.

  • A𝑦=56𝑥+15
  • B𝑦=−65𝑥+4
  • C𝑦=3𝑥−1
  • D𝑦=𝑥+4

Q8:

Lines 𝐴 and 𝐵 are perpendicular to each other and meet at (−1,4). If the slope of 𝐴 is 0, what is the equation of line 𝐵?

  • A𝑦=−1
  • B𝑥=−1
  • C𝑦=0
  • D𝑥=4
  • E𝑦=4

Q9:

Determine whether the lines 𝑦=−17𝑥−5 and 𝑦=−17𝑥−1 are parallel, perpendicular, or neither.

  • Aperpendicular
  • Bparallel
  • Cneither

Q10:

If a line 𝐿 is perpendicular to the line −2𝑦+10=−6𝑥+7, and 𝐿 passes through the points 𝐴(𝑛,−10) and 𝐵(−7,2), what is the value of 𝑛?

This lesson includes 34 additional questions and 306 additional question variations for subscribers.

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