Lesson Worksheet: Equations of Parallel and Perpendicular Lines Mathematics

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 6𝑥𝑦+4=0.

  • A𝑦=6𝑥7
  • B𝑦=6𝑥5
  • 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=38𝑥258
  • C𝑦=6𝑥+83
  • D𝑦=83𝑥+6
  • E𝑦=83𝑥6

Q3:

A straight line 𝐿 has the equation 𝑦=2𝑥3. 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=2𝑥1
  • E𝑦=12𝑥+72

Q4:

Find, in slope-intercept form, the equation of the line perpendicular to 𝑦=2𝑥4 that passes through the point 𝐴(3,3).

  • A𝑦=12𝑥32
  • B𝑦=2𝑥9
  • 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=1916𝑥13516
  • E𝑦=1619𝑥34119

Q6:

Write, in the form 𝑦=𝑚𝑥+𝑐, the equation of the line that is parallel to the line 4𝑥+7𝑦4=0 and that intercepts the 𝑦-axis at 1.

  • A𝑦=𝑥4
  • 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=3𝑥1
  • 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=17𝑥5 and 𝑦=17𝑥1 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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