Lesson Worksheet: Equations of Parallel and Perpendicular Lines Mathematics • 11th Grade

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


If lines 𝑦=π‘Žπ‘₯+𝑏 and 𝑦=𝑐π‘₯+𝑑 are perpendicular, which of the following products equals βˆ’1?

  • A𝑏 and 𝑑
  • Bπ‘Ž and 𝑑
  • C𝑏 and 𝑐
  • Dπ‘Ž and 𝑐


Determine whether the lines 𝑦=βˆ’17π‘₯βˆ’5 and 𝑦=βˆ’17π‘₯βˆ’1 are parallel, perpendicular, or neither.

  • Aperpendicular
  • Bparallel
  • Cneither


Which of the following lines is perpendicular to the line 19π‘₯βˆ’3𝑦=5?

  • A3𝑦=1βˆ’19π‘₯
  • B3π‘₯βˆ’19𝑦=5
  • C2βˆ’19𝑦=3π‘₯
  • D3+19𝑦=2π‘₯
  • E3𝑦=19π‘₯+4


Which axis is the straight line π‘₯=5 parallel to?

  • Aπ‘₯-axis
  • B𝑦-axis


Find, in slope–intercept form, the equation of the straight line passing through the point (3,1) and parallel to the straight line passing through the two points (1,βˆ’1) and (4,βˆ’3).

  • A𝑦=βˆ’32π‘₯+112
  • B𝑦=23π‘₯βˆ’1
  • C𝑦=βˆ’23π‘₯+3
  • D𝑦=βˆ’23π‘₯+1
  • E𝑦=32π‘₯βˆ’72


Find, in slope-intercept form, the equation of the line perpendicular to 𝑦=2π‘₯βˆ’4 that passes through the point 𝐴(3,βˆ’3).

  • A𝑦=βˆ’12π‘₯βˆ’32
  • B𝑦=2π‘₯βˆ’9
  • C𝑦=βˆ’12π‘₯+32
  • D𝑦=βˆ’32π‘₯+12
  • E𝑦=2π‘₯+9


Determine, in slope-intercept form, the equation of the line passing through 𝐴(13,βˆ’7) perpendicular to the line passing through 𝐡(8,βˆ’9) and 𝐢(βˆ’8,10).

  • A𝑦=βˆ’1916π‘₯+13516
  • B𝑦=1619π‘₯+34119
  • C𝑦=βˆ’34119π‘₯+1619
  • D𝑦=βˆ’1916π‘₯βˆ’13516
  • E𝑦=1619π‘₯βˆ’34119


The straight lines 8π‘₯+5𝑦=8 and 8π‘₯+π‘Žπ‘¦=βˆ’8 are parallel. What is the value of π‘Ž?


If the two straight lines πΏβˆΆβˆ’8π‘₯+7π‘¦βˆ’9=0 and πΏβˆΆπ‘Žπ‘₯+24𝑦+56=0 are perpendicular, find the value of π‘Ž.


Describe the relation between the straight lines 4π‘₯βˆ’4𝑦=5 and 32π‘₯βˆ’32𝑦=40.

  • AThey are coincident.
  • BThey are parallel.
  • CThey are perpendicular.

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