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(𝑥2)
  • B𝑦3=4𝑥+2
  • C𝑦+3=4𝑥2
  • D𝑦3=4(𝑥2)
  • E𝑦+3=4(𝑥+2)

Q2:

Write the equation represented by the graph shown. Give your answer in the form 𝑦𝑎=𝑚(𝑥𝑏).

  • A𝑦+2=12(𝑥6)
  • B𝑦6=2(𝑥+2)
  • C𝑦6=12(𝑥+2)
  • D𝑦6=12(𝑥+2)
  • E𝑦+2=2(𝑥6)

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(𝑥1)
  • B𝑦10=27(𝑥+1)
  • C𝑦10=27(𝑥+1)
  • D𝑦+10=27(𝑥1)
  • 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).

  • A𝑦6=2𝑥1
  • B𝑦6=2(𝑥1)
  • C𝑦6=2(𝑥1)
  • D𝑦6=2𝑥1
  • E𝑦+6=2(𝑥1)

Q5:

Write the equation represented by the graph shown. Give your answer in the form 𝑦𝑎=𝑚(𝑥𝑏).

  • A𝑦2=13(𝑥5)
  • B𝑦5=3(𝑥2)
  • C𝑦5=3(𝑥2)
  • D𝑦5=13(𝑥2)
  • E𝑦2=3(𝑥5)

Q6:

Write the equation represented by the graph shown. Give your answer in the form 𝑦𝑎=𝑚(𝑥𝑏).

  • A𝑦1=43(𝑥3)
  • B𝑦3=43(𝑥1)
  • C𝑦1=34(𝑥3)
  • D𝑦1=43(𝑥3)
  • E𝑦3=34(𝑥1)

Q7:

Which of the following graphs represents the equation 𝑦+1=2(𝑥4)?

  • A
  • B
  • C
  • D
  • E

Q8:

Which of the following graphs represents the equation 𝑦2=4(𝑥1)?

  • A
  • B
  • C
  • D
  • E

Q9:

Which of the following graphs represents the equation 𝑦5=23(𝑥3)?

  • 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
𝑦7121722
  • 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?

  • A4𝑦3𝑥=12
  • B3𝑦4𝑥=12
  • C3𝑦4𝑥=12
  • D3𝑦+4𝑥=12
  • E4𝑦3𝑥=12

Q13:

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

  • A𝑥+2𝑦=0
  • B𝑦2𝑥=0
  • C𝑥2𝑦=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.

  • A𝑥𝑦=5
  • B𝑥𝑦=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
  • D7𝑥2𝑦=9

Q20:

Does the equation 6𝑥2𝑦=1 represent a straight line?

  • AYes
  • BNo

Q21:

Given that the line 2𝑥8𝑦=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?

  • A6𝑥8𝑦=2
  • B2𝑥𝑦=6
  • C𝑥+7𝑦=3
  • D8𝑥+𝑦=0

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