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Year 8 Gradient and Linear Equations Worksheet — Level 2 — 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 2 — 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.For the line y = −5x + 2, write the gradient and the y-intercept.

Answer: gradient −5; 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.

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

Answer: y = −2x − 2

  1. y = −2x + (y-intercept)
  2. −6 = −2 × 2 + (y-intercept)
  3. y-intercept = −6 − (−4) = −2
  4. y = −2x − 2
3.Find the gradient of the line through (1, 4) and (5, 3).

Answer: −

  1. gradient = rise ÷ run = (3 − 4) ÷ (5 − 1)
  2. = −1 ÷ 4 = −
4.A line has a gradient of 1 and passes through (−4, −2). Find its equation.

Answer: y = x + 2

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

Answer: 2

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

Answer: gradient −4; 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.

7.For the line y = −4x + 2, write the gradient and the y-intercept.

Answer: gradient −4; 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.

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

Answer: gradient −2; 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.

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

Answer: gradient −4; 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.

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

Answer: gradient 3; y-intercept 4

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

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