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Worksheet: Linear Equations in Point-Slope Form

In this worksheet, we will practice writing linear equations in point-slope form for a line of a known slope that contains the point (h,k).

Q1:

Find, in point-slope form, the equation of the graph with slope 4 that passes through the point ( 2 , βˆ’ 3 ) .

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

Q2:

Write the equation represented by the graph shown. Give your answer in the form 𝑦 βˆ’ π‘Ž = π‘š ( π‘₯ βˆ’ 𝑏 ) .

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

Q3:

Find, in point-slope form, the equation of the line with slope 2 7 that passes through the point 𝐴 ( 1 , βˆ’ 1 0 ) .

  • A 𝑦 + 1 0 = βˆ’ 2 7 ( π‘₯ βˆ’ 1 )
  • B 𝑦 βˆ’ 1 0 = 2 7 ( π‘₯ + 1 )
  • C 𝑦 βˆ’ 1 0 = βˆ’ 2 7 ( π‘₯ + 1 )
  • D 𝑦 + 1 0 = 2 7 ( π‘₯ βˆ’ 1 )
  • E 𝑦 + 1 0 = 2 7 ( π‘₯ + 1 )

Q4:

Write the equation of the line of gradient 10 through the point in the form .

  • A
  • B
  • C
  • D
  • E

Q5:

Which of the following is a point on the line 𝑦 = 1 3 π‘₯ βˆ’ 4 ?

  • A ( βˆ’ 3 , βˆ’ 4 )
  • B ( 6 , βˆ’ 1 )
  • C ( 1 , βˆ’ 3 )
  • D ( 3 , βˆ’ 3 )
  • E ( 0 , 4 )

Q6:

A line 𝐿 has a slope of 1 3 and passes through the point ( 1 , 1 ) . Work out the equation of the line, giving your answer in the form 𝑦 = π‘š π‘₯ + 𝑐 .

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

Q7:

Which of the following graphs represents the equation 𝑦 βˆ’ 5 = 2 3 ( π‘₯ βˆ’ 3 ) ?

  • A
  • B
  • C
  • D
  • E

Q8:

Write the equation represented by the graph shown. Give your answer in the form 𝑦 βˆ’ π‘Ž = π‘š ( π‘₯ βˆ’ 𝑏 ) .

  • A 𝑦 βˆ’ 5 = 1 3 ( π‘₯ βˆ’ 2 )
  • B 𝑦 βˆ’ 2 = 3 ( π‘₯ βˆ’ 5 )
  • C 𝑦 βˆ’ 2 = 1 3 ( π‘₯ βˆ’ 5 )
  • D 𝑦 βˆ’ 5 = 3 ( π‘₯ βˆ’ 2 )
  • E 𝑦 βˆ’ 5 = βˆ’ 3 ( π‘₯ βˆ’ 2 )

Q9:

Write, in the form , the equation of the line of gradient that meets the -axis at the point .

  • A
  • B
  • C
  • D
  • E

Q10:

Find, in point-slope form, the equation of the graph with slope βˆ’ 2 that passes through the point (1, 6).

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

Q11:

Determine the equation of the line which passes through point ( βˆ’ 7 , βˆ’ 8 ) and is perpendicular to the line meeting the π‘₯ -axis at 9 and the 𝑦 -axis at 1.

  • A π‘₯ βˆ’ 9 𝑦 βˆ’ 5 5 = 0
  • B 9 π‘₯ + 𝑦 βˆ’ 5 5 = 0
  • C 9 π‘₯ + 𝑦 + 5 5 = 0
  • D 9 π‘₯ βˆ’ 𝑦 + 5 5 = 0

Q12:

Write the equation represented by the graph shown. Give your answer in the form 𝑦 βˆ’ π‘Ž = π‘š ( π‘₯ βˆ’ 𝑏 ) .

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

Q13:

Which of the following graphs represents the equation 𝑦 + 1 = 2 ( π‘₯ βˆ’ 4 ) ?

  • A
  • B
  • C
  • D
  • E

Q14:

Which of the following graphs represents the equation 𝑦 βˆ’ 2 = 4 ( π‘₯ βˆ’ 1 ) ?

  • A
  • B
  • C
  • D
  • E

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