Lesson Worksheet: Equation of a Straight Line: Standard and Point–Slope Forms Mathematics • 9th Grade

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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).

  • A𝑦+3=4(𝑥−2)
  • B𝑦−3=4𝑥+2
  • C𝑦+3=4𝑥−2
  • D𝑦−3=4(𝑥−2)
  • E𝑦+3=4(𝑥+2)

Q2:

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

  • A𝑦+2=12(𝑥−6)
  • B𝑦−6=2(𝑥+2)
  • C𝑦−6=−12(𝑥+2)
  • D𝑦−6=12(𝑥+2)
  • E𝑦+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).

  • A𝑦+10=−27(𝑥−1)
  • B𝑦−10=27(𝑥+1)
  • C𝑦−10=−27(𝑥+1)
  • D𝑦+10=27(𝑥−1)
  • E𝑦+10=27(𝑥+1)

Q4:

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

  • A𝑦−6=2𝑥−1
  • B𝑦−6=−2(𝑥−1)
  • C𝑦−6=2(𝑥−1)
  • D𝑦−6=−2𝑥−1
  • E𝑦+6=−2(𝑥−1)

Q5:

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

  • A𝑦−2=13(𝑥−5)
  • B𝑦−5=−3(𝑥−2)
  • C𝑦−5=3(𝑥−2)
  • D𝑦−5=13(𝑥−2)
  • E𝑦−2=3(𝑥−5)

Q6:

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

  • A𝑦−1=−43(𝑥−3)
  • B𝑦−3=43(𝑥−1)
  • C𝑦−1=34(𝑥−3)
  • D𝑦−1=43(𝑥−3)
  • E𝑦−3=34(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-intercept and 𝑦-intercept.

𝑥7142128
𝑦−7−12−17−22
  • A𝑥-intercept coordinate: −145,0, 𝑦-intercept coordinate: (0,−2)
  • B𝑥-intercept coordinate: 145,0, 𝑦-intercept coordinate: (0,2)
  • C𝑥-intercept coordinate: −514,0, 𝑦-intercept coordinate: (0,−2)
  • D𝑥-intercept coordinate: 0,−145, 𝑦-intercept coordinate: (−2,0)
  • E𝑥-intercept coordinate: 0,145, 𝑦-intercept coordinate: (−2,0)

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