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Year 8 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers

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

1.Find the gradient of the line through (−1, −1) and (1, −10).

Answer: −

  1. gradient = rise ÷ run = (−10 − (−1)) ÷ (1 − (−1))
  2. = −9 ÷ 2 = −
2.Find the gradient of the line through (3, 3) and (5, −3).

Answer: −3

  1. gradient = rise ÷ run = (−3 − 3) ÷ (5 − 3)
  2. = −6 ÷ 2 = −3
3.For the line y = −3x, write the gradient and the y-intercept.

Answer: gradient −3; 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.

4.For the line y = 6x + 5, write the gradient and the y-intercept.

Answer: gradient 6; 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.

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

Answer: y = x + 4

  1. y = 1x + (y-intercept)
  2. 3 = 1 × (−1) + (y-intercept)
  3. y-intercept = 3 − (−1) = 4
  4. y = x + 4
6.Find the gradient of the line through (−5, 2) and (0, 8).

Answer:

  1. gradient = rise ÷ run = (8 − 2) ÷ (0 − (−5))
  2. = 6 ÷ 5 =
7.For the line y = x − 4, write the gradient and the y-intercept.

Answer: gradient 1; 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.

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

Answer: gradient −1; 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.

9.Find the gradient of the line through (−5, 1) and (−6, 4).

Answer: −3

  1. gradient = rise ÷ run = (4 − 1) ÷ (−6 − (−5))
  2. = 3 ÷ −1 = −3
10.A line has a gradient of 5 and passes through (−4, −21). Find its equation.

Answer: y = 5x − 1

  1. y = 5x + (y-intercept)
  2. −21 = 5 × (−4) + (y-intercept)
  3. y-intercept = −21 − (−20) = −1
  4. y = 5x − 1
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