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

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

1.Does the point (−1, 2) lie on the line y = −3x − 4?
  1. AYes
  2. BNo

Answer: No

Substitute x = −1: y = −3 × (−1) − 4 = −1, not 2.

2.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.

3.Does the point (4, 23) lie on the line y = 5x?
  1. AYes
  2. BNo

Answer: No

Substitute x = 4: y = 5 × 4 + 0 = 20, not 23.

4.For the line y = 4x + 8, write the gradient and the y-intercept.

Answer: gradient 4; y-intercept 8

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.For the line y = −6x + 8, write the gradient and the y-intercept.

Answer: gradient −6; y-intercept 8

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

6.A line has a gradient of 4 and passes through (−1, −13). Find its equation.

Answer: y = 4x − 9

  1. y = 4x + (y-intercept)
  2. −13 = 4 × (−1) + (y-intercept)
  3. y-intercept = −13 − (−4) = −9
  4. y = 4x − 9
7.A line has a gradient of 2 and passes through (3, 8). Find its equation.

Answer: y = 2x + 2

  1. y = 2x + (y-intercept)
  2. 8 = 2 × 3 + (y-intercept)
  3. y-intercept = 8 − 6 = 2
  4. y = 2x + 2
8.For the line y = 3x − 9, write the gradient and the y-intercept.

Answer: gradient 3; y-intercept −9

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

9.A line has a gradient of −1 and passes through (4, −10). Find its equation.

Answer: y = −x − 6

  1. y = −1x + (y-intercept)
  2. −10 = −1 × 4 + (y-intercept)
  3. y-intercept = −10 − (−4) = −6
  4. y = −x − 6
10.A line has a gradient of −1 and passes through (−3, 10). Find its equation.

Answer: y = −x + 7

  1. y = −1x + (y-intercept)
  2. 10 = −1 × (−3) + (y-intercept)
  3. y-intercept = 10 − 3 = 7
  4. y = −x + 7
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