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Worksheet: Finding the Equation of a Straight Line in Different Forms given the Slope and a Point on It

Q1:

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

Q2:

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 )

Q3:

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

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:

A quadrilateral has its vertices at the points 𝐴 ( βˆ’ 5 , 3 ) , 𝐡 ( 0 , βˆ’ 2 ) , 𝐢 ( βˆ’ 2 , βˆ’ 6 ) , and 𝐷 ( βˆ’ 8 , βˆ’ 2 ) . A point 𝐸 lies on 𝐴 𝐢 such that the lengths of 𝐴 𝐸 and 𝐢 𝐸 are in the ratio of 1 ∢ 2 , and a point 𝐹 lies on 𝐡 𝐷 such that the lengths of 𝐡 𝐹 and 𝐷 𝐹 are in the ratio of 1 ∢ 3 .

Find the coordinates of 𝐸 .

  • A ( βˆ’ 3 , βˆ’ 3 )
  • B ( 0 , βˆ’ 4 )
  • C ( 0 , βˆ’ 3 )
  • D ( βˆ’ 4 , 0 )
  • E ( 0 , βˆ’ 1 )

Find the coordinates of 𝐹 .

  • A ( βˆ’ 2 , βˆ’ 2 )
  • B ( βˆ’ 2 , 0 )
  • C ( βˆ’ 4 , βˆ’ 2 )
  • D ( βˆ’ 6 , βˆ’ 2 )
  • E ( βˆ’ 4 , 0 )

Find the slope of the line βƒ–     βƒ— 𝐸 𝐹 .

Find the equation of the line βƒ–     βƒ— 𝐸 𝐹 , giving your answer in the form 𝑦 = π‘š π‘₯ + 𝑐 .

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

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:

33. 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