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Worksheet: Standard Form of a Line

Q1:

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

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

Q2:

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

  • A 2 π‘₯ βˆ’ 𝑦 + 1 6 = 0
  • B π‘₯ + 2 𝑦 + 1 6 = 0
  • C βˆ’ π‘₯ + 2 𝑦 βˆ’ 1 6 = 0
  • D βˆ’ π‘₯ + 2 𝑦 + 1 6 = 0

Q3:

Given 𝐴 ( 2 , 1 ) , 𝐡 ( βˆ’ 9 , βˆ’ 6 ) , and 𝐢 ( 1 , 6 ) , find the general equation of the straight line that passes through point 𝐴 and bisects 𝐡 𝐢 .

  • A 6 π‘₯ βˆ’ 𝑦 βˆ’ 4 = 0
  • B π‘₯ + 6 𝑦 βˆ’ 4 = 0
  • C βˆ’ π‘₯ + 6 𝑦 + 4 = 0
  • D βˆ’ π‘₯ + 6 𝑦 βˆ’ 4 = 0

Q4:

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

  • A 7 π‘₯ + 6 𝑦 + 1 0 = 0
  • B βˆ’ 6 π‘₯ + 7 𝑦 βˆ’ 3 8 = 0
  • C 6 π‘₯ + 7 𝑦 βˆ’ 3 8 = 0
  • D 6 π‘₯ + 7 𝑦 + 1 0 = 0

Q5:

Find the Cartesian equation of the straight line passing through the point ( βˆ’ 3 , βˆ’ 5 ) and parallel to the straight line whose equation is 5 π‘₯ + 5 𝑦 + 9 = 0 .

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

Q6:

Write the equation represented by the graph shown. Give your answer in the form π‘Ž π‘₯ + 𝑏 𝑦 = 𝑐 .

  • A 3 π‘₯ + 4 𝑦 = βˆ’ 3 6
  • B 4 π‘₯ βˆ’ 3 𝑦 = 3 6
  • C 4 π‘₯ + 3 𝑦 = 3 6
  • D 3 π‘₯ βˆ’ 4 𝑦 = 3 6
  • E 3 π‘₯ βˆ’ 4 𝑦 = βˆ’ 3 6

Q7:

Write the equation represented by the graph shown. Give your answer in the form π‘Ž π‘₯ + 𝑏 𝑦 = 𝑐 .

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

Q8:

A line has gradient and passes through the point . What is the equation of this line?

  • A
  • B
  • C
  • D

Q9:

A line has gradient 2 and passes through the point . What is the equation of this line?

  • A
  • B
  • C
  • D

Q10:

A line has gradient and passes through the point . What is the equation of this line?

  • A
  • B
  • C
  • D