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Worksheet: Equation of a Straight Line in Different Forms

Q1:

Determine the equation of the line passing through 𝐴 ( 0 , 1 6 ) and 𝐡 ( 1 , βˆ’ 9 ) in slope-intercept form.

  • A 𝑦 = βˆ’ 2 5 π‘₯ βˆ’ 1 6
  • B 𝑦 = 1 6 π‘₯ βˆ’ 2 5
  • C 𝑦 = 1 6 π‘₯ + 2 5
  • D 𝑦 = βˆ’ 2 5 π‘₯ + 1 6
  • E 𝑦 = π‘₯ βˆ’ 2 5

Q2:

A line 𝐿 has a slope of βˆ’ 2 and passes through the point ( 2 , βˆ’ 3 ) . Work out the equation of the line, giving your answer in the form 𝑦 = π‘š π‘₯ + 𝑐 .

  • A 𝑦 = 2 π‘₯ βˆ’ 3
  • B 𝑦 = 2 π‘₯ + 2
  • C 𝑦 = 2 π‘₯ βˆ’ 7
  • D 𝑦 = βˆ’ 2 π‘₯ + 1
  • E 𝑦 = 2 π‘₯ βˆ’ 4

Q3:

Find the point of intersection between the 𝑦 -axis and the line with slope π‘š that passes through the point ( π‘Ž , 0 ) .

  • A ( 0 , π‘Ž )
  • B ( 0 , π‘š π‘Ž )
  • C ( 0 , βˆ’ π‘Ž )
  • D ( 0 , βˆ’ π‘š π‘Ž )
  • E ( βˆ’ π‘Ž , 0 )

Q4:

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

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

Q5:

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

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

Q6:

A line 𝐿 has a slope of 3 and passes through the point ( 3 , 4 ) . Work out the equation of the line, giving your answer in the form 𝑦 = π‘š π‘₯ + 𝑐 .

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

Q7:

Find, in slope-intercept form, the equation of the graph with 𝑦 -intercept βˆ’ 2 and slope 7.

  • A 𝑦 = 2 π‘₯ βˆ’ 7
  • B 𝑦 = βˆ’ 2 π‘₯ + 7
  • C 𝑦 = 7 π‘₯ + 2
  • D 𝑦 = 7 π‘₯ βˆ’ 2
  • E 𝑦 = βˆ’ 2 π‘₯ βˆ’ 7