Worksheet: Equations of Horizontal, Parallel, and Perpendicular Straight Lines

In this worksheet, we will practice finding the equation of a straight line that is either horizontal, parallel, or perpendicular to another line.

Q1:

Which of the following lines is perpendicular to the line 1 9 𝑥 3 𝑦 = 5 ?

  • A 3 𝑦 = 1 1 9 𝑥
  • B 3 𝑥 1 9 𝑦 = 5
  • C 3 𝑦 = 1 9 𝑥 + 4
  • D 2 1 9 𝑦 = 3 𝑥
  • E 3 + 1 9 𝑦 = 2 𝑥

Q2:

Lines 𝐴 and 𝐵 are perpendicular to each other and meet at ( 1 , 4 ) . If the slope of 𝐴 is 3 2 , what is the equation of line 𝐵 ?

  • A 𝑦 = 3 2 ( 𝑥 + 1 ) + 4
  • B 𝑦 = 3 2 ( 𝑥 1 ) 4
  • C 𝑦 = 3 2 ( 𝑥 + 1 ) 4
  • D 𝑦 = 3 2 ( 𝑥 1 ) + 4
  • E 𝑦 = ( 𝑥 1 ) + 4

Q3:

Consider the graph:

Which of the following could be the equation of the line?

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

Q4:

Which axis is the straight line 𝑦 = 3 parallel to?

  • A 𝑥 -axis
  • B 𝑦 -axis

Q5:

Write, in the form 𝑦 = 𝑚 𝑥 + 𝑐 , the equation of the line that is perpendicular to the line 5 𝑥 + 2 𝑦 = 6 and that intercepts the 𝑥 -axis at 20.

  • A 𝑦 = 2 0 𝑥 2 5
  • B 𝑦 = 5 2 𝑥 2 0
  • C 𝑦 = 2 5 𝑥 2 0
  • D 𝑦 = 2 5 𝑥 8
  • E 𝑦 = 5 2 𝑥 6

Q6:

Write, in the form 𝑦 = 𝑚 𝑥 + 𝑐 , the equation of the line through 𝐴 ( 5 , 8 ) that is perpendicular to 𝐴 𝐵 , where 𝐵 ( 8 , 3 ) .

  • A 𝑦 = 5 1 3 𝑥 7 9 1 3
  • B 𝑦 = 5 1 3 𝑥 2 1
  • C 𝑦 = 1 3 5 𝑥 7 9 1 3
  • D 𝑦 = 1 3 5 𝑥 2 1
  • E 𝑦 = 1 3 5 𝑥 8

Q7:

In the figure below, 𝐿 𝐿 and 𝐴 𝐵 = 8 length units. If the equation of 𝐿 is 𝑦 = 4 5 𝑥 + 4 , find the equation of 𝐿 .

  • A 𝑦 = 4 5 𝑥 + 8
  • B 𝑦 = 4 𝑥 + 4
  • C 𝑦 = 4 𝑥
  • D 𝑦 = 4 5 𝑥 4

Q8:

Find the equation of the straight line passing through the point ( 1 , 1 ) and perpendicular to the straight line passing through the points ( 9 , 9 ) and ( 6 , 3 ) .

  • A 𝑦 = 2 𝑥 1
  • B 𝑦 = 2 𝑥 + 3
  • C 𝑦 = 4 5 𝑥 1 5
  • D 𝑦 = 5 4 𝑥 + 9 4

Q9:

If the straight line passing through the two points ( 2 , 8 ) and ( 3 , 3 ) is perpendicular to the straight line whose equation is 3 𝑥 + 𝑘 𝑦 + 8 = 0 , find the value of 𝑘 .

  • A 1 1 5
  • B33
  • C5
  • D 1 5

Q10:

If the two straight lines 𝐿 8 𝑥 + 7 𝑦 9 = 0 and 𝐿 𝑎 𝑥 + 2 4 𝑦 + 5 6 = 0 are perpendicular, find the value of 𝑎 .

Q11:

The straight lines 8 𝑥 + 5 𝑦 = 8 and 8 𝑥 + 𝑎 𝑦 = 8 are parallel. What is the value of 𝑎 ?

Q12:

The line 𝑦 = ( 𝑎 + 5 ) 𝑥 6 is perpendicular to the line through points ( 8 , 2 ) and ( 2 , 5 ) . What is 𝑎 ?

Q13:

The square 𝐴 𝐵 𝐶 𝐷 has an area of 13, and the corner 𝐵 has coordinates ( 2 , 1 ) . Give the equation of 𝐶 𝑂 in the form 𝑦 = 𝑚 𝑥 + 𝑐 .

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

Q14:

Given 𝐴 ( 4 , 4 ) and 𝐵 ( 2 , 4 ) , find the equation of the perpendicular to 𝐴 𝐵 that passes through the midpoint of this line segment. Give your answer in the form 𝑦 = 𝑚 𝑥 + 𝑐 .

  • A 𝑦 = 1 4 𝑥 + 3 2
  • B 𝑦 = 4 𝑥 1 2
  • C 𝑦 = 3 4 𝑥 1 4
  • D 𝑦 = 1 4 𝑥 + 3 4

Q15:

The line 4 𝑥 3 𝑦 2 4 = 0 meets the 𝑥 - and 𝑦 -axis at points 𝐴 and 𝐵 respectively. Find the equation of the line perpendicular to 𝐴 𝐵 and passing through its midpoint.

  • A 4 𝑥 + 3 𝑦 + 7 = 0
  • B 3 𝑥 4 𝑦 7 = 0
  • C 3 𝑥 4 𝑦 + 7 = 0
  • D 3 𝑥 + 4 𝑦 + 7 = 0

Q16:

Given 𝐴 ( 2 , 7 ) and 𝐵 ( 8 , 1 ) , what is the perpendicular bisector of the segment 𝐴 𝐵 ?

  • A 4 𝑥 5 𝑦 3 = 0
  • B 5 𝑥 + 4 𝑦 3 = 0
  • C 5 𝑥 + 4 𝑦 + 3 = 0
  • D 5 𝑥 4 𝑦 + 3 = 0

Q17:

Let 𝐴 and 𝐵 be the 𝑥 - and 𝑦 -intercepts of the line 5 𝑥 3 𝑦 6 = 0 . Give the equation of the line parallel to the 𝑦 -axis that passes through the midpoint of 𝐴 𝐵 .

  • A 𝑦 = 3 5
  • B 𝑥 = 1
  • C 𝑦 = 3 5 𝑥
  • D 𝑥 = 3 5

Q18:

Which axis is the straight line 𝑟 = ( 2 , 5 ) + 𝐾 ( 0 , 1 ) parallel to?

  • A 𝑦 -axis
  • B 𝑥 -axis

Q19:

If lines 𝑦 = 𝑎 𝑥 + 𝑏 and 𝑦 = 𝑐 𝑥 + 𝑑 are perpendicular, which of the following products equals 1 ?

  • A 𝑏 and 𝑐
  • B 𝑎 and 𝑑
  • C 𝑏 and 𝑑
  • D 𝑎 and 𝑐

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