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

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,βˆ’3).

  • A𝑦+3=4(π‘₯βˆ’2)
  • Bπ‘¦βˆ’3=4π‘₯+2
  • C𝑦+3=4π‘₯βˆ’2
  • Dπ‘¦βˆ’3=4(π‘₯βˆ’2)
  • E𝑦+3=4(π‘₯+2)

Q2:

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

  • A𝑦+2=12(π‘₯βˆ’6)
  • Bπ‘¦βˆ’6=2(π‘₯+2)
  • Cπ‘¦βˆ’6=βˆ’12(π‘₯+2)
  • Dπ‘¦βˆ’6=12(π‘₯+2)
  • E𝑦+2=2(π‘₯βˆ’6)

Q3:

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

  • A𝑦+10=βˆ’27(π‘₯βˆ’1)
  • Bπ‘¦βˆ’10=27(π‘₯+1)
  • Cπ‘¦βˆ’10=βˆ’27(π‘₯+1)
  • D𝑦+10=27(π‘₯βˆ’1)
  • E𝑦+10=27(π‘₯+1)

Q4:

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

  • Aπ‘¦βˆ’6=2π‘₯βˆ’1
  • Bπ‘¦βˆ’6=βˆ’2(π‘₯βˆ’1)
  • Cπ‘¦βˆ’6=2(π‘₯βˆ’1)
  • Dπ‘¦βˆ’6=βˆ’2π‘₯βˆ’1
  • E𝑦+6=βˆ’2(π‘₯βˆ’1)

Q5:

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

  • Aπ‘¦βˆ’2=13(π‘₯βˆ’5)
  • Bπ‘¦βˆ’5=βˆ’3(π‘₯βˆ’2)
  • Cπ‘¦βˆ’5=3(π‘₯βˆ’2)
  • Dπ‘¦βˆ’5=13(π‘₯βˆ’2)
  • Eπ‘¦βˆ’2=3(π‘₯βˆ’5)

Q6:

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

  • Aπ‘¦βˆ’1=βˆ’43(π‘₯βˆ’3)
  • Bπ‘¦βˆ’3=43(π‘₯βˆ’1)
  • Cπ‘¦βˆ’1=34(π‘₯βˆ’3)
  • Dπ‘¦βˆ’1=43(π‘₯βˆ’3)
  • Eπ‘¦βˆ’3=34(π‘₯βˆ’1)

Q7:

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

  • A
  • B
  • C
  • D
  • E

Q8:

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

  • A
  • B
  • C
  • D
  • E

Q9:

Which of the following graphs represents the equation π‘¦βˆ’5=23(π‘₯βˆ’3)?

  • A
  • B
  • C
  • D
  • E

Q10:

The points in the table belong to the same line. Find the coordinates of the π‘₯- and 𝑦-intercepts.

π‘₯7142128
π‘¦βˆ’7βˆ’12βˆ’17βˆ’22
  • Aπ‘₯-intercept coordinate: ο€Όβˆ’145,0, 𝑦-intercept coordinate: (0,βˆ’2)
  • Bπ‘₯-intercept coordinate: ο€Ό145,0, 𝑦-intercept coordinate: (0,2)
  • Cπ‘₯-intercept coordinate: ο€Όβˆ’514,0, 𝑦-intercept coordinate: (0,βˆ’2)
  • Dπ‘₯-intercept coordinate: ο€Ό0,βˆ’145, 𝑦-intercept coordinate: (βˆ’2,0)
  • Eπ‘₯-intercept coordinate: ο€Ό0,145, 𝑦-intercept coordinate: (βˆ’2,0)

Q11:

What are the coordinates of the π‘₯- and 𝑦-intercepts of this line?

  • Aπ‘₯-intercept at ο€Ό12,0, 𝑦-intercept at ο€Ό0,βˆ’117
  • Bπ‘₯-intercept at ο€Όβˆ’328,0, 𝑦-intercept at ο€Ό0,βˆ’113
  • Cπ‘₯-intercept at ο€Όβˆ’14,0, 𝑦-intercept at ο€Ό0,17
  • Dπ‘₯-intercept at ο€Όβˆ’12,0, 𝑦-intercept at ο€Ό0,117

Q12:

What is the equation of the line with π‘₯-intercept βˆ’3 and 𝑦-intercept 4?

  • A4π‘¦βˆ’3π‘₯=βˆ’12
  • B3π‘¦βˆ’4π‘₯=βˆ’12
  • C3π‘¦βˆ’4π‘₯=12
  • D3𝑦+4π‘₯=12
  • E4π‘¦βˆ’3π‘₯=12

Q13:

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

  • Aπ‘₯+2𝑦=0
  • Bπ‘¦βˆ’2π‘₯=0
  • Cπ‘₯βˆ’2𝑦=0
  • D𝑦+2π‘₯=0

Q14:

Which of the following graphs represents the equation 3π‘₯+2𝑦=12?

  • A
  • B
  • C
  • D
  • E

Q15:

Which of the following graphs represents the equation π‘₯+𝑦=3?

  • A
  • B
  • C
  • D

Q16:

Write the equation represented by the graph shown. Give your answer in the form π‘₯+𝑦=𝑐.

  • Aπ‘₯βˆ’π‘¦=βˆ’5
  • Bπ‘₯βˆ’π‘¦=5
  • Cπ‘₯+𝑦=βˆ’5
  • Dπ‘₯+𝑦=5

Q17:

Find the coordinates of the 𝑦-intercept and the slope of the straight line whose equation is βˆ’54π‘₯+2𝑦=9.

  • A(0,9), 54
  • Bο€Ό0,βˆ’365, 85
  • C(0,9), 25
  • Dο€Ό0,92, βˆ’58
  • Eο€Ό0,92, 58

Q18:

The graph of the equation 𝑦+2=5(π‘₯+1) is a straight line.

What is the slope of the line?

Which one of the following points lies on the line?

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

Q19:

Which of the following equations represents a straight line?

  • Aπ‘₯+βˆšπ‘¦=βˆ’5
  • B𝑦=√π‘₯+6
  • C𝑦+1π‘₯=βˆ’8
  • Dβˆ’7π‘₯βˆ’2𝑦=βˆ’9

Q20:

Does the equation 6π‘₯βˆ’2𝑦=1 represent a straight line?

  • Ayes
  • Bno

Q21:

Given that the line 2π‘₯βˆ’8𝑦=π‘Ž intersects the π‘₯-axis at the point (βˆ’4,𝑏), find the values of π‘Ž and 𝑏.

  • Aπ‘Ž=0, 𝑏=βˆ’8
  • Bπ‘Ž=βˆ’8, 𝑏=0
  • Cπ‘Ž=βˆ’4, 𝑏=βˆ’8
  • Dπ‘Ž=32, 𝑏=0

Q22:

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

  • A6π‘₯βˆ’8𝑦=2
  • Bβˆ’2π‘₯βˆ’π‘¦=6
  • Cπ‘₯+7𝑦=3
  • Dβˆ’8π‘₯+𝑦=0

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