Worksheet: Equation of a Straight Line: Slope–Intercept Form

In this worksheet, we will practice finding the equation of a straight line in slope–intercept form given particular information, including its slope, its y-intercept, points on it, or its graph.

Q1:

Which equation represents the line shown?

  • A𝑦=π‘₯5+2
  • B𝑦=5π‘₯+12
  • C𝑦=π‘₯2+5
  • D𝑦=2π‘₯+5
  • E𝑦=π‘₯2βˆ’5

Q2:

Find the equation of the straight line represented by the graph below in the form of 𝑦=π‘šπ‘₯+𝑐.

  • A𝑦=8π‘₯βˆ’9
  • B𝑦=βˆ’2π‘₯+3
  • C𝑦=βˆ’83π‘₯+53
  • D𝑦=2π‘₯βˆ’3
  • E𝑦=βˆ’8π‘₯βˆ’9

Q3:

Find the equation of the line with π‘₯-intercept 3 and 𝑦-intercept 7, and calculate the area of the triangle on this line and the two coordinate axes.

  • A𝑦=310π‘₯βˆ’7, area of triangle = 10.5 square units
  • B𝑦=βˆ’73π‘₯+7, area of triangle = 21 square units
  • C𝑦=βˆ’73π‘₯+7, area of triangle = 10.5 square units
  • D𝑦=βˆ’37π‘₯+7, area of triangle = 21 square units

Q4:

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

  • A𝑦=βˆ’23π‘₯βˆ’4
  • B𝑦=23π‘₯βˆ’4
  • C𝑦=βˆ’32π‘₯βˆ’4
  • D𝑦=βˆ’32π‘₯+4
  • E𝑦=32π‘₯βˆ’4

Q5:

Determine, in slope-intercept form, the equation of the line which has a slope of 8 and a 𝑦-intercept of βˆ’4.

  • A𝑦=βˆ’4π‘₯βˆ’8
  • B𝑦=π‘₯βˆ’4
  • C𝑦=8π‘₯βˆ’4
  • D𝑦=8π‘₯+4
  • E𝑦=βˆ’4π‘₯+8

Q6:

Find the coordinates of the point where 𝑦=4π‘₯+12 intersects the 𝑦-axis.

  • A(4,0)
  • B(4,βˆ’3)
  • C(0,12)
  • D(0,βˆ’3)

Q7:

Which of the following graphs represents the equation 𝑦=βˆ’5π‘₯βˆ’2?

  • A
  • B
  • C
  • D
  • E

Q8:

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

  • A
  • B
  • C
  • D
  • E

Q9:

Find the equation, in the form 𝑦=π‘šπ‘₯+𝑐, of the line with slope βˆ’83 and 𝑦-intercept 10.

  • A𝑦=βˆ’83π‘₯+10
  • B𝑦=βˆ’38π‘₯+10
  • C𝑦=83π‘₯+10
  • D𝑦=10π‘₯βˆ’83

Q10:

Does the point (4,βˆ’11) lie on the line 𝑦=βˆ’2π‘₯βˆ’4?

  • Ayes
  • Bno

Q11:

Does the point (2,βˆ’3) lie on the line 𝑦=5π‘₯βˆ’7?

  • Ayes
  • Bno

Q12:

Does the point ο€Ό1,βˆ’92 lie on the line 𝑦=12π‘₯βˆ’5?

  • Ano
  • Byes

Q13:

What is the slope of the line that passes through the point (4,18) and intercepts 𝑦 at βˆ’2?

Q14:

The points in this table lie on a line. Find the equation of the line in slope-intercept form.

π‘₯5101520
π‘¦βˆ’8βˆ’15βˆ’22βˆ’29
  • A𝑦=βˆ’75π‘₯βˆ’1
  • B𝑦=βˆ’32π‘₯βˆ’15
  • C𝑦=βˆ’57π‘₯βˆ’57
  • D𝑦=βˆ’57π‘₯βˆ’1
  • E𝑦=βˆ’75π‘₯βˆ’57

Q15:

Which of the following is the Cartesian equation of the line through (π‘Ž,0) with slope π‘š?

  • A𝑦=π‘₯+π‘Ž
  • B𝑦=π‘Žπ‘₯βˆ’π‘š
  • C𝑦=π‘šπ‘₯βˆ’π‘šπ‘Ž
  • D𝑦=βˆ’π‘šπ‘₯βˆ’π‘šπ‘Ž
  • E𝑦=π‘šπ‘₯+π‘Ž

Q16:

Determine the equation of the line passing through 𝐴(0,16) and 𝐡(1,βˆ’9) in slope-intercept form.

  • A𝑦=βˆ’25π‘₯+16
  • B𝑦=π‘₯βˆ’25
  • C𝑦=16π‘₯+25
  • D𝑦=βˆ’25π‘₯βˆ’16
  • E𝑦=16π‘₯βˆ’25

Q17:

A line 𝐿 has a slope of βˆ’2 and passes through the point (2,βˆ’3). Work out the equation of the line, giving your answer in the form 𝑦=π‘šπ‘₯+𝑐.

  • A𝑦=2π‘₯βˆ’4
  • B𝑦=2π‘₯βˆ’7
  • C𝑦=βˆ’2π‘₯+1
  • D𝑦=2π‘₯+2
  • E𝑦=2π‘₯βˆ’3

Q18:

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

  • A𝑦=βˆ’43π‘₯βˆ’2
  • B𝑦=βˆ’34π‘₯+2
  • C𝑦=43π‘₯+2
  • D𝑦=βˆ’43π‘₯+2
  • E𝑦=34π‘₯+2

Q19:

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

  • A𝑦=βˆ’13π‘₯+2
  • B𝑦=βˆ’3π‘₯+2
  • C𝑦=3π‘₯+2
  • D𝑦=2π‘₯βˆ’3
  • E𝑦=3π‘₯βˆ’2

Q20:

A line 𝐿 has a slope of 3 and passes through the point (3,4). Work out the equation of the line, giving your answer in the form 𝑦=π‘šπ‘₯+𝑐.

  • A𝑦=3π‘₯βˆ’9
  • B𝑦=3π‘₯βˆ’5
  • C𝑦=3π‘₯βˆ’3
  • D𝑦=3π‘₯+5
  • E𝑦=3π‘₯+3

Q21:

Find, in slope-intercept form, the equation of the graph with 𝑦-intercept βˆ’2 and slope 7.

  • A𝑦=2π‘₯βˆ’7
  • B𝑦=7π‘₯+2
  • C𝑦=βˆ’2π‘₯+7
  • D𝑦=βˆ’2π‘₯βˆ’7
  • E𝑦=7π‘₯βˆ’2

Q22:

A line 𝐿 passes through the points (2,3) and (βˆ’2,5). Work out the equation of the line, giving your answer in the form 𝑦=π‘šπ‘₯+𝑐.

  • A𝑦=βˆ’2π‘₯+7
  • B𝑦=2π‘₯βˆ’1
  • C𝑦=βˆ’12π‘₯+4
  • D𝑦=12π‘₯+14
  • E𝑦=12π‘₯+2

Q23:

A line 𝐿 passes through the points (1,1) and (βˆ’5,βˆ’1). Work out the equation of the line, giving your answer in the form 𝑦=π‘šπ‘₯+𝑐.

  • A𝑦=βˆ’3π‘₯+4
  • B𝑦=3π‘₯+2
  • C𝑦=13π‘₯βˆ’2
  • D𝑦=13π‘₯+23
  • E𝑦=π‘₯βˆ’2

Q24:

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

  • A𝑦=4π‘₯+2
  • B𝑦=βˆ’2π‘₯+4
  • C𝑦=2π‘₯+4
  • D𝑦=βˆ’2π‘₯βˆ’4
  • E𝑦=12π‘₯+4

Q25:

Write the equation of the line passing through (2,14) and (βˆ’4,βˆ’4).

  • A𝑦=3π‘₯+8
  • B𝑦=π‘₯3+403
  • C𝑦=3π‘₯βˆ’8
  • D𝑦=π‘₯3+8
  • E𝑦=8π‘₯+3

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