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Year 8 Gradient and Linear Equations Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 8 linear relationships & graphs worksheet.

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Year 8 Gradient and Linear Equations Worksheet — Level 3 — Answers

Show your working. Gradient = rise ÷ run; the equation of a line can be written as y = (gradient)x + (y-intercept).

1.For the line y = 2x + 3, write the gradient and the y-intercept.

Answer: gradient 2; y-intercept 3

In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.

2.Does the point (3, 15) lie on the line y = 5x?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = 3: y = 5 × 3 + 0 = 15, which matches.

3.For the line y = −6x − 2, write the gradient and the y-intercept.

Answer: gradient −6; y-intercept −2

In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.

4.For the line y = 3x + 6, write the gradient and the y-intercept.

Answer: gradient 3; y-intercept 6

In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.

5.A line has a gradient of 4 and passes through (−3, −20). Find its equation.

Answer: y = 4x − 8

  1. y = 4x + (y-intercept)
  2. −20 = 4 × (−3) + (y-intercept)
  3. y-intercept = −20 − (−12) = −8
  4. y = 4x − 8
6.A line has a gradient of −2 and passes through (−1, 6). Find its equation.

Answer: y = −2x + 4

  1. y = −2x + (y-intercept)
  2. 6 = −2 × (−1) + (y-intercept)
  3. y-intercept = 6 − 2 = 4
  4. y = −2x + 4
7.For the line y = 2x − 5, write the gradient and the y-intercept.

Answer: gradient 2; y-intercept −5

In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.

8.Does the point (2, 9) lie on the line y = 2x + 5?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = 2: y = 2 × 2 + 5 = 9, which matches.

9.For the line y = 6x, write the gradient and the y-intercept.

Answer: gradient 6; y-intercept 0

In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.

10.A line has a gradient of 1 and passes through (2, 6). Find its equation.

Answer: y = x + 4

  1. y = 1x + (y-intercept)
  2. 6 = 1 × 2 + (y-intercept)
  3. y-intercept = 6 − 2 = 4
  4. y = x + 4
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