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

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)

Q11:

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

  • A𝑥-intercept at 12,0, 𝑦-intercept at 0,−117
  • B𝑥-intercept at −328,0, 𝑦-intercept at 0,−113
  • C𝑥-intercept at −14,0, 𝑦-intercept at 0,17
  • D𝑥-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?

  • A4𝑦−3𝑥=−12
  • B3𝑦−4𝑥=−12
  • C3𝑦−4𝑥=12
  • D3𝑦+4𝑥=12
  • E4𝑦−3𝑥=12

Q13:

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

  • A𝑥+2𝑦=0
  • B𝑦−2𝑥=0
  • C𝑥−2𝑦=0
  • D𝑦+2𝑥=0

Q14:

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

  • A
  • B
  • C
  • D
  • E

Q15:

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

  • A
  • B
  • C
  • D

Q16:

Write the equation represented by the graph shown. Give your answer in the form 𝑥+𝑦=𝑐.

  • A𝑥−𝑦=−5
  • B𝑥−𝑦=5
  • C𝑥+𝑦=−5
  • D𝑥+𝑦=5

Q17:

Find the coordinates of the 𝑦-intercept and the slope of the straight line whose equation is −54𝑥+2𝑦=9.

  • A(0,9), 54
  • B0,−365, 85
  • C(0,9), 25
  • D0,92, −58
  • E0,92, 58

Q18:

The graph of the equation 𝑦+2=5(𝑥+1) is a straight line.

What is the slope of the line?

Which one of the following points lies on the line?

  • A(−2,5)
  • B(5,−2)
  • C(−2,−1)
  • D(1,5)
  • E(−1,−2)

Q19:

Which of the following equations represents a straight line?

  • A𝑥+√𝑦=−5
  • B𝑦=√𝑥+6
  • C𝑦+1𝑥=−8
  • D−7𝑥−2𝑦=−9

Q20:

Does the equation 6𝑥−2𝑦=1 represent a straight line?

  • AYes
  • BNo

Q21:

Given that the line 2𝑥−8𝑦=𝑎 intersects the 𝑥-axis at the point (−4,𝑏), find the values of 𝑎 and 𝑏.

  • A𝑎=0, 𝑏=−8
  • B𝑎=−8, 𝑏=0
  • C𝑎=−4, 𝑏=−8
  • D𝑎=32, 𝑏=0

Q22:

Which of the following equations represents a line through the origin?

  • A6𝑥−8𝑦=2
  • B−2𝑥−𝑦=6
  • C𝑥+7𝑦=3
  • D−8𝑥+𝑦=0

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