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Year 8 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 2 — 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 2 — 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 (4, −8) lie on the line y = −x − 3?
  1. AYes
  2. BNo

Answer: No

Substitute x = 4: y = −1 × 4 − 3 = −7, not −8.

2.A line has a gradient of 2 and passes through (−1, −9). Find its equation.

Answer: y = 2x − 7

  1. y = 2x + (y-intercept)
  2. −9 = 2 × (−1) + (y-intercept)
  3. y-intercept = −9 − (−2) = −7
  4. y = 2x − 7
3.For the line y = x − 7, write the gradient and the y-intercept.

Answer: gradient 1; y-intercept −7

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.A line has a gradient of −5 and passes through (−4, 16). Find its equation.

Answer: y = −5x − 4

  1. y = −5x + (y-intercept)
  2. 16 = −5 × (−4) + (y-intercept)
  3. y-intercept = 16 − 20 = −4
  4. y = −5x − 4
5.For the line y = −x − 2, write the gradient and the y-intercept.

Answer: gradient −1; 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.

6.A line has a gradient of 2 and passes through (2, 11). Find its equation.

Answer: y = 2x + 7

  1. y = 2x + (y-intercept)
  2. 11 = 2 × 2 + (y-intercept)
  3. y-intercept = 11 − 4 = 7
  4. y = 2x + 7
7.For the line y = 5x − 6, write the gradient and the y-intercept.

Answer: gradient 5; 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.

8.A line has a gradient of −3 and passes through (1, −2). Find its equation.

Answer: y = −3x + 1

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

Answer: gradient −6; y-intercept −1

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.Does the point (−4, −6) lie on the line y = 4x + 7?
  1. AYes
  2. BNo

Answer: No

Substitute x = −4: y = 4 × (−4) + 7 = −9, not −6.

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