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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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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Linear Relationships & Graphs

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

Answer: 1

  1. gradient = rise ÷ run = (−1 − (−4)) ÷ (4 − 1)
  2. = 3 ÷ 3 = 1
2.For the line y = 3x − 3, write the gradient and the y-intercept.

Answer: gradient 3; 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.

3.Find the gradient of the line through (2, 4) and (6, 10).

Answer:

  1. gradient = rise ÷ run = (10 − 4) ÷ (6 − 2)
  2. = 6 ÷ 4 =
4.Find the gradient of the line through (−4, 5) and (−5, 2).

Answer: 3

  1. gradient = rise ÷ run = (2 − 5) ÷ (−5 − (−4))
  2. = −3 ÷ −1 = 3
5.A line has a gradient of 5 and passes through (2, 18). Find its equation.

Answer: y = 5x + 8

  1. y = 5x + (y-intercept)
  2. 18 = 5 × 2 + (y-intercept)
  3. y-intercept = 18 − 10 = 8
  4. y = 5x + 8
6.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.

7.For the line y = −6x + 3, write the gradient and the y-intercept.

Answer: gradient −6; 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.

8.Find the gradient of the line through (−3, 2) and (0, 10).

Answer:

  1. gradient = rise ÷ run = (10 − 2) ÷ (0 − (−3))
  2. = 8 ÷ 3 =
9.For the line y = 5x, write the gradient and the y-intercept.

Answer: gradient 5; 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.

10.A line has a gradient of −5 and passes through (0, 6). Find its equation.

Answer: y = −5x + 6

  1. y = −5x + (y-intercept)
  2. 6 = −5 × 0 + (y-intercept)
  3. y-intercept = 6 − 0 = 6
  4. y = −5x + 6
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