Worksheet: Standard Form of a Line

In this worksheet, we will practice representing the equation of a line in standard form.

Q1:

Write the equation represented by the graph shown. Give your answer in the form 𝑎 𝑥 + 𝑏 𝑦 = 𝑐 .

  • A 3 𝑥 + 4 𝑦 = 3 6
  • B 4 𝑥 3 𝑦 = 3 6
  • C 4 𝑥 + 3 𝑦 = 3 6
  • D 3 𝑥 4 𝑦 = 3 6
  • E 3 𝑥 4 𝑦 = 3 6

Q2:

Write the equation represented by the graph shown. Give your answer in the form 𝑎 𝑥 + 𝑏 𝑦 = 𝑐 .

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

Q3:

A line has slope 3 2 and passes through the point ( 5 , 0 ) . What is the equation of this line?

  • A 2 𝑥 + 3 𝑦 1 5 = 0
  • B 3 𝑥 7 𝑦 1 5 = 0
  • C 3 𝑥 + 2 𝑦 + 1 5 = 0
  • D 3 𝑥 + 2 𝑦 1 5 = 0

Q4:

Find the Cartesian equation of the straight line passing through the point ( 4 , 2 ) and parallel to the straight line whose equation is 6 𝑥 + 7 𝑦 + 3 = 0 .

  • A 7 𝑥 + 6 𝑦 + 1 0 = 0
  • B 6 𝑥 + 7 𝑦 3 8 = 0
  • C 6 𝑥 + 7 𝑦 3 8 = 0
  • D 6 𝑥 + 7 𝑦 + 1 0 = 0

Q5:

Given 𝐴 ( 0 , 8 ) , 𝐵 ( 5 , 8 ) , and 𝐶 ( 9 , 6 ) , find the general equation of the straight line that passes through point 𝐴 and bisects 𝐵 𝐶 .

  • A 2 𝑥 𝑦 + 1 6 = 0
  • B 𝑥 + 2 𝑦 + 1 6 = 0
  • C 𝑥 + 2 𝑦 1 6 = 0
  • D 𝑥 + 2 𝑦 + 1 6 = 0

Q6:

Find the equation of the straight line that passes through the points ( 1 , 1 ) and ( 3 , 4 ) . Give your answer in standard form.

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

Q7:

Given 𝐴 ( 2 , 1 ) , 𝐵 ( 9 , 6 ) , and 𝐶 ( 1 , 6 ) , find the general equation of the straight line that passes through point 𝐴 and bisects 𝐵 𝐶 .

  • A 6 𝑥 𝑦 4 = 0
  • B 𝑥 + 6 𝑦 4 = 0
  • C 𝑥 + 6 𝑦 + 4 = 0
  • D 𝑥 + 6 𝑦 4 = 0

Q8:

Find the Cartesian equation of the straight line passing through the point ( 3 , 5 ) and parallel to the straight line whose equation is 5 𝑥 + 5 𝑦 + 9 = 0 .

  • A 𝑥 + 𝑦 + 8 = 0
  • B 𝑥 + 𝑦 + 2 = 0
  • C 𝑥 + 𝑦 + 2 = 0
  • D 𝑥 + 𝑦 + 8 = 0

Q9:

A line has slope 2 and passes through the point ( 3 , 0 ) . What is the equation of this line?

  • A 𝑥 2 𝑦 6 = 0
  • B 𝑥 + 2 𝑦 + 3 = 0
  • C 2 𝑥 𝑦 6 = 0
  • D 2 𝑥 𝑦 + 6 = 0

Q10:

A line has slope 1 4 and passes through the point ( 7 , 0 ) . What is the equation of this line?

  • A 4 𝑥 + 𝑦 + 7 = 0
  • B 3 𝑥 + 2 𝑦 + 2 1 = 0
  • C 𝑥 + 4 𝑦 7 = 0
  • D 𝑥 + 4 𝑦 + 7 = 0

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