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Year 8 Gradient and Linear Equations Worksheet — Level 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 2 — 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 = x − 3, write the gradient and the y-intercept.

Answer: gradient 1; 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.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.

3.Find the gradient of the line through (−1, −4) and (4, 1).

Answer: 1

  1. gradient = rise ÷ run = (1 − (−4)) ÷ (4 − (−1))
  2. = 5 ÷ 5 = 1
4.A line has a gradient of 1 and passes through (−1, 7). Find its equation.

Answer: y = x + 8

  1. y = 1x + (y-intercept)
  2. 7 = 1 × (−1) + (y-intercept)
  3. y-intercept = 7 − (−1) = 8
  4. y = x + 8
5.For the line y = 4x + 4, write the gradient and the y-intercept.

Answer: gradient 4; 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.

6.Find the gradient of the line through (1, 5) and (5, 7).

Answer:

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

Answer: gradient −5; 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.A line has a gradient of 5 and passes through (−4, −12). Find its equation.

Answer: y = 5x + 8

  1. y = 5x + (y-intercept)
  2. −12 = 5 × (−4) + (y-intercept)
  3. y-intercept = −12 − (−20) = 8
  4. y = 5x + 8
9.Find the gradient of the line through (−6, 6) and (−2, 3).

Answer: −

  1. gradient = rise ÷ run = (3 − 6) ÷ (−2 − (−6))
  2. = −3 ÷ 4 = −
10.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.

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