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

Q1:

Consider the graph:

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

  • A 𝑦 = βˆ’ 1 3 π‘₯ βˆ’ 2
  • B 𝑦 = 1 3 π‘₯ + 2
  • C 𝑦 = βˆ’ 1 3 π‘₯ + 2
  • D 𝑦 = 1 3 π‘₯ βˆ’ 2
  • E 𝑦 = 1 3 π‘₯ + 1 2

Q2:

If the two straight lines 𝐿 ∢ βˆ’ 8 π‘₯ + 7 𝑦 βˆ’ 9 = 0 1 and 𝐿 ∢ π‘Ž π‘₯ + 2 4 𝑦 + 5 6 = 0 2 are perpendicular, find the value of π‘Ž .

Q3:

Which of the following lines is perpendicular to the line 1 9 π‘₯ βˆ’ 3 𝑦 = 5 ?

  • A 3 𝑦 = 1 βˆ’ 1 9 π‘₯
  • B 3 π‘₯ βˆ’ 1 9 𝑦 = 5
  • C 3 𝑦 = 1 9 π‘₯ + 4
  • D 2 βˆ’ 1 9 𝑦 = 3 π‘₯
  • E 3 + 1 9 𝑦 = 2 π‘₯

Q4:

Given 𝐴 ( 4 , 4 ) and 𝐡 ( 2 , βˆ’ 4 ) , find the equation of the perpendicular to 𝐴 𝐡 that passes through the midpoint of this line segment. Give your answer in the form 𝑦 = π‘š π‘₯ + 𝑐 .

  • A 𝑦 = βˆ’ 1 4 π‘₯ + 3 2
  • B 𝑦 = 4 π‘₯ βˆ’ 1 2
  • C 𝑦 = 3 4 π‘₯ βˆ’ 1 4
  • D 𝑦 = βˆ’ 1 4 π‘₯ + 3 4

Q5:

Write, in the form 𝑦 = π‘š π‘₯ + 𝑐 , the equation of the line through 𝐴 ( 5 , βˆ’ 8 ) that is perpendicular to 𝐴 𝐡 , where 𝐡 ( βˆ’ 8 , βˆ’ 3 ) .

  • A 𝑦 = βˆ’ 5 1 3 π‘₯ βˆ’ 7 9 1 3
  • B 𝑦 = βˆ’ 5 1 3 π‘₯ βˆ’ 2 1
  • C 𝑦 = βˆ’ 1 3 5 π‘₯ βˆ’ 7 9 1 3
  • D 𝑦 = 1 3 5 π‘₯ βˆ’ 2 1
  • E 𝑦 = 1 3 5 π‘₯ βˆ’ 8

Q6:

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

  • A 𝑦 = βˆ’ 2 π‘₯ βˆ’ 1
  • B 𝑦 = βˆ’ 2 π‘₯ + 3
  • C 𝑦 = βˆ’ 4 5 π‘₯ βˆ’ 1 5
  • D 𝑦 = 5 4 π‘₯ + 9 4

Q7:

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

  • A 𝑦 = βˆ’ 3 2 ( π‘₯ + 1 ) + 4
  • B 𝑦 = 3 2 ( π‘₯ βˆ’ 1 ) βˆ’ 4
  • C 𝑦 = 3 2 ( π‘₯ + 1 ) βˆ’ 4
  • D 𝑦 = βˆ’ 3 2 ( π‘₯ βˆ’ 1 ) + 4
  • E 𝑦 = βˆ’ ( π‘₯ βˆ’ 1 ) + 4

Q8:

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

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 π‘₯ + π‘˜ 𝑦 + 8 = 0 , find the value of π‘˜ .

  • A βˆ’ 1 1 5
  • B33
  • C5
  • D βˆ’ 1 5

Q10:

Which axis is the straight line parallel to?

  • A -axis
  • B -axis

Q11:

The line 4 π‘₯ βˆ’ 3 𝑦 βˆ’ 2 4 = 0 meets the π‘₯ - and 𝑦 -axis at points 𝐴 and 𝐡 respectively. Find the equation of the line perpendicular to 𝐴 𝐡 and passing through its midpoint.

  • A 4 π‘₯ + 3 𝑦 + 7 = 0
  • B 3 π‘₯ βˆ’ 4 𝑦 βˆ’ 7 = 0
  • C 3 π‘₯ βˆ’ 4 𝑦 + 7 = 0
  • D 3 π‘₯ + 4 𝑦 + 7 = 0

Q12:

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

  • A 4 π‘₯ βˆ’ 5 𝑦 βˆ’ 3 = 0
  • B 5 π‘₯ + 4 𝑦 βˆ’ 3 = 0
  • C 5 π‘₯ + 4 𝑦 + 3 = 0
  • D 5 π‘₯ βˆ’ 4 𝑦 + 3 = 0

Q13:

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

  • A π‘₯ -axis
  • B 𝑦 -axis

Q14:

Write, in the form 𝑦 = π‘š π‘₯ + 𝑐 , the equation of the line that is perpendicular to the line βˆ’ 5 π‘₯ + 2 𝑦 = βˆ’ 6 and that intercepts the π‘₯ -axis at 20.

  • A 𝑦 = βˆ’ 2 0 π‘₯ βˆ’ 2 5
  • B 𝑦 = 5 2 π‘₯ βˆ’ 2 0
  • C 𝑦 = βˆ’ 2 5 π‘₯ βˆ’ 2 0
  • D 𝑦 = βˆ’ 2 5 π‘₯ βˆ’ 8
  • E 𝑦 = 5 2 π‘₯ βˆ’ 6

Q15:

Let 𝐴 and 𝐡 be the π‘₯ - and 𝑦 -intercepts of the line 5 π‘₯ βˆ’ 3 𝑦 βˆ’ 6 = 0 . Give the equation of the line parallel to the 𝑦 -axis that passes through the midpoint of 𝐴 𝐡 .

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

Q16:

In the figure below, and length units. If the equation of is , find the equation of .

  • A
  • B
  • C
  • D

Q17:

The square 𝐴 𝐡 𝐢 𝐷 has an area of 13, and the corner 𝐡 has coordinates ( 2 , 1 ) . Give the equation of βƒ–     βƒ— 𝐢 𝑂 in the form 𝑦 = π‘š π‘₯ + 𝑐 .

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

Q18:

The line 𝑦 = ( π‘Ž + 5 ) π‘₯ βˆ’ 6 is perpendicular to the line through points ( βˆ’ 8 , 2 ) and ( βˆ’ 2 , 5 ) . What is π‘Ž ?

Q19:

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

  • A 𝑏 and 𝑐
  • B π‘Ž and 𝑑
  • C 𝑏 and 𝑑
  • D π‘Ž and 𝑐