Worksheet: Equation of a Straight Line: Standard and Point–Slope Forms

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In this worksheet, we will practice finding the equation of a line in standard and point–slope forms given two points, a slope and a point, or a graph.

Q1:

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

  • A 𝑦 + 3 = 4 ( 𝑥 − 2 )
  • B 𝑦 − 3 = 4 𝑥 + 2
  • C 𝑦 + 3 = 4 𝑥 − 2
  • D 𝑦 − 3 = 4 ( 𝑥 − 2 )
  • E 𝑦 + 3 = 4 ( 𝑥 + 2 )

Q2:

Write the equation represented by the graph shown. Give your answer in the form 𝑦−𝑎=𝑚(𝑥−𝑏).

  • A 𝑦 + 2 = 1 2 ( 𝑥 − 6 )
  • B 𝑦 − 6 = 2 ( 𝑥 + 2 )
  • C 𝑦 − 6 = − 1 2 ( 𝑥 + 2 )
  • D 𝑦 − 6 = 1 2 ( 𝑥 + 2 )
  • E 𝑦 + 2 = 2 ( 𝑥 − 6 )

Q3:

Find, in point-slope form, the equation of the line with slope 27 that passes through the point 𝐴(1,−10).

  • A 𝑦 + 1 0 = − 2 7 ( 𝑥 − 1 )
  • B 𝑦 − 1 0 = 2 7 ( 𝑥 + 1 )
  • C 𝑦 − 1 0 = − 2 7 ( 𝑥 + 1 )
  • D 𝑦 + 1 0 = 2 7 ( 𝑥 − 1 )
  • E 𝑦 + 1 0 = 2 7 ( 𝑥 + 1 )

Q4:

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

  • A 𝑦 − 6 = 2 𝑥 − 1
  • B 𝑦 − 6 = − 2 ( 𝑥 − 1 )
  • C 𝑦 − 6 = 2 ( 𝑥 − 1 )
  • D 𝑦 − 6 = − 2 𝑥 − 1
  • E 𝑦 + 6 = − 2 ( 𝑥 − 1 )

Q5:

Write the equation represented by the graph shown. Give your answer in the form 𝑦−𝑎=𝑚(𝑥−𝑏).

  • A 𝑦 − 2 = 1 3 ( 𝑥 − 5 )
  • B 𝑦 − 5 = − 3 ( 𝑥 − 2 )
  • C 𝑦 − 5 = 3 ( 𝑥 − 2 )
  • D 𝑦 − 5 = 1 3 ( 𝑥 − 2 )
  • E 𝑦 − 2 = 3 ( 𝑥 − 5 )

Q6:

Write the equation represented by the graph shown. Give your answer in the form 𝑦−𝑎=𝑚(𝑥−𝑏).

  • A 𝑦 − 1 = − 4 3 ( 𝑥 − 3 )
  • B 𝑦 − 3 = 4 3 ( 𝑥 − 1 )
  • C 𝑦 − 1 = 3 4 ( 𝑥 − 3 )
  • D 𝑦 − 1 = 4 3 ( 𝑥 − 3 )
  • E 𝑦 − 3 = 3 4 ( 𝑥 − 1 )

Q7:

Which of the following graphs represents the equation 𝑦+1=2(𝑥−4)?

  • A
  • B
  • C
  • D
  • E

Q8:

Which of the following graphs represents the equation 𝑦−2=4(𝑥−1)?

  • A
  • B
  • C
  • D
  • E

Q9:

Which of the following graphs represents the equation 𝑦−5=23(𝑥−3)?

  • A
  • B
  • C
  • D
  • E

Q10:

The points in the table belong to the same line. Find the coordinates of the 𝑥- and 𝑦-intercepts.

𝑥 7 14 21 28
𝑦 − 7 − 1 2 − 1 7 − 2 2
  • A 𝑥 -intercept coordinate: −145,0, 𝑦-intercept coordinate: (0,−2)
  • B 𝑥 -intercept coordinate: 145,0, 𝑦-intercept coordinate: (0,2)
  • C 𝑥 -intercept coordinate: −514,0, 𝑦-intercept coordinate: (0,−2)
  • D 𝑥 -intercept coordinate: 0,−145, 𝑦-intercept coordinate: (−2,0)
  • E 𝑥 -intercept coordinate: 0,145, 𝑦-intercept coordinate: (−2,0)

Q11:

What are the coordinates of the 𝑥- and 𝑦-intercepts of this line?

  • A 𝑥 -intercept at 12,0, 𝑦-intercept at 0,−117
  • B 𝑥 -intercept at −328,0, 𝑦-intercept at 0,−113
  • C 𝑥 -intercept at −14,0, 𝑦-intercept at 0,17
  • D 𝑥 -intercept at −12,0, 𝑦-intercept at 0,117

Q12:

What is the equation of the line with 𝑥-intercept −3 and 𝑦-intercept 4?

  • A 4 𝑦 − 3 𝑥 = − 1 2
  • B 3 𝑦 − 4 𝑥 = − 1 2
  • C 3 𝑦 − 4 𝑥 = 1 2
  • D 3 𝑦 + 4 𝑥 = 1 2
  • E 4 𝑦 − 3 𝑥 = 1 2

Q13:

Determine the equation of the straight line given in the diagram.

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

Q14:

Which of the following graphs represents the equation 3𝑥+2𝑦=12?

  • A
  • B