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 its slope and its y-intercept, two points on it, or its graph.

Q1:

Which equation represents the line shown?

  • A 𝑦 = π‘₯ 5 + 2
  • B 𝑦 = π‘₯ 2 βˆ’ 5
  • C 𝑦 = π‘₯ 2 + 5
  • D 𝑦 = 2 π‘₯ + 5
  • E 𝑦 = 5 π‘₯ + 1 2

Q2:

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

  • A 𝑦 = βˆ’ 8 π‘₯ βˆ’ 9
  • B 𝑦 = 8 π‘₯ βˆ’ 9
  • C 𝑦 = 2 π‘₯ βˆ’ 3
  • D 𝑦 = βˆ’ 8 3 π‘₯ + 5 3
  • E 𝑦 = βˆ’ 2 π‘₯ + 3

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.

  • A 𝑦 = 3 1 0 π‘₯ βˆ’ 7 , area of triangle = 10.5 square units
  • B 𝑦 = βˆ’ 7 3 π‘₯ + 7 , area of triangle = 10.5 square units
  • C 𝑦 = βˆ’ 7 3 π‘₯ + 7 , area of triangle = 21 square units
  • D 𝑦 = βˆ’ 3 7 π‘₯ + 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.

  • A 𝑦 = βˆ’ 3 2 π‘₯ + 4
  • B 𝑦 = βˆ’ 2 3 π‘₯ βˆ’ 4
  • C 𝑦 = βˆ’ 3 2 π‘₯ βˆ’ 4
  • D 𝑦 = 2 3 π‘₯ βˆ’ 4
  • E 𝑦 = 3 2 π‘₯ 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.

  • A 𝑦 = βˆ’ 4 π‘₯ βˆ’ 8
  • B 𝑦 = π‘₯ βˆ’ 4
  • C 𝑦 = 8 π‘₯ βˆ’ 4
  • D 𝑦 = 8 π‘₯ + 4
  • E 𝑦 = βˆ’ 4 π‘₯ + 8

Q6:

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

  • A ( 0 , βˆ’ 3 )
  • B ( 4 , 0 )
  • C ( 4 , βˆ’ 3 )
  • D ( 0 , 1 2 )

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.

  • A 𝑦 = βˆ’ 3 8 π‘₯ + 1 0
  • B 𝑦 = βˆ’ 8 3 π‘₯ + 1 0
  • C 𝑦 = 8 3 π‘₯ + 1 0
  • D 𝑦 = 1 0 π‘₯ βˆ’ 8 3

Q10:

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

  • Ano
  • Byes

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‘₯ 5 10 15 20
𝑦 βˆ’ 8 βˆ’ 1 5 βˆ’ 2 2 βˆ’ 2 9
  • A 𝑦 = βˆ’ 5 7 π‘₯ βˆ’ 5 7
  • B 𝑦 = βˆ’ 3 2 π‘₯ βˆ’ 1 5
  • C 𝑦 = βˆ’ 7 5 π‘₯ βˆ’ 1
  • D 𝑦 = βˆ’ 7 5 π‘₯ βˆ’ 5 7
  • E 𝑦 = βˆ’ 5 7 π‘₯ βˆ’ 1

Q15:

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

  • A 𝑦 = π‘š π‘₯ βˆ’ π‘š π‘Ž
  • B 𝑦 = π‘š π‘₯ + π‘Ž
  • C 𝑦 = βˆ’ π‘š π‘₯ βˆ’ π‘š π‘Ž
  • D 𝑦 = π‘Ž π‘₯ βˆ’ π‘š
  • E 𝑦 = π‘₯ + π‘Ž

Q16:

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

  • A 𝑦 = βˆ’ 2 5 π‘₯ + 1 6
  • B 𝑦 = 1 6 π‘₯ βˆ’ 2 5
  • C 𝑦 = 1 6 π‘₯ + 2 5
  • D 𝑦 = π‘₯ βˆ’ 2 5
  • E 𝑦 = βˆ’ 2 5 π‘₯ βˆ’ 1 6

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.

  • A 𝑦 = 2 π‘₯ + 2
  • B 𝑦 = 2 π‘₯ βˆ’ 7
  • C 𝑦 = 2 π‘₯ βˆ’ 4
  • D 𝑦 = 2 π‘₯ βˆ’ 3
  • E 𝑦 = βˆ’ 2 π‘₯ + 1

Q18:

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

  • A 𝑦 = βˆ’ 4 3 π‘₯ βˆ’ 2
  • B 𝑦 = βˆ’ 3 4 π‘₯ + 2
  • C 𝑦 = 4 3 π‘₯ + 2
  • D 𝑦 = βˆ’ 4 3 π‘₯ + 2
  • E 𝑦 = 3 4 π‘₯ + 2

Q19:

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

  • A 𝑦 = βˆ’ 1 3 π‘₯ + 2
  • B 𝑦 = βˆ’ 3 π‘₯ + 2
  • C 𝑦 = 3 π‘₯ + 2
  • D 𝑦 = 2 π‘₯ βˆ’ 3
  • E 𝑦 = 3 π‘₯ 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.

  • A 𝑦 = 3 π‘₯ βˆ’ 9
  • B 𝑦 = 3 π‘₯ βˆ’ 5
  • C 𝑦 = 3 π‘₯ βˆ’ 3
  • D 𝑦 = 3 π‘₯ + 5
  • E 𝑦 = 3 π‘₯ + 3

Q21:

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

  • A 𝑦 = βˆ’ 2 π‘₯ βˆ’ 7
  • B 𝑦 = 7 π‘₯ + 2
  • C 𝑦 = 2 π‘₯ βˆ’ 7
  • D 𝑦 = βˆ’ 2 π‘₯ + 7
  • E 𝑦 = 7 π‘₯ 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.

  • A 𝑦 = βˆ’ 1 2 π‘₯ + 4
  • B 𝑦 = 1 2 π‘₯ + 2
  • C 𝑦 = βˆ’ 2 π‘₯ + 7
  • D 𝑦 = 1 2 π‘₯ + 1 4
  • E 𝑦 = 2 π‘₯ βˆ’ 1

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.

  • A 𝑦 = βˆ’ 3 π‘₯ + 4
  • B 𝑦 = 3 π‘₯ + 2
  • C 𝑦 = 1 3 π‘₯ βˆ’ 2
  • D 𝑦 = 1 3 π‘₯ + 2 3
  • E 𝑦 = π‘₯ βˆ’ 2

Q24:

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

  • A 𝑦 = 4 π‘₯ + 2
  • B 𝑦 = βˆ’ 2 π‘₯ + 4
  • C 𝑦 = 2 π‘₯ + 4
  • D 𝑦 = βˆ’ 2 π‘₯ βˆ’ 4
  • E 𝑦 = 1 2 π‘₯ + 4

Q25:

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

  • A 𝑦 = 3 π‘₯ + 8
  • B 𝑦 = π‘₯ 3 + 4 0 3
  • C 𝑦 = 3 π‘₯ βˆ’ 8
  • D 𝑦 = π‘₯ 3 + 8
  • E 𝑦 = 8 π‘₯ + 3

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