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Year 9 Gradient and Linear Equations Worksheet — Level 1 — Practice Set 2 — Answers

Answer sheet with worked solutions for the Year 9 linear relationships & graphs worksheet.

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Year 9 Gradient and Linear Equations Worksheet — Level 1 — 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.For the line y = −x − 1, write the gradient and the y-intercept.

Answer: gradient −1; 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.

2.Find the gradient of the line through (−2, −1) and (3, 4).

Answer: 1

  1. gradient = rise ÷ run = (4 − (−1)) ÷ (3 − (−2))
  2. = 5 ÷ 5 = 1
3.Find the gradient of the line through (−5, 6) and (−8, −3).

Answer: 3

  1. gradient = rise ÷ run = (−3 − 6) ÷ (−8 − (−5))
  2. = −9 ÷ −3 = 3
4.Find the gradient of the line through (5, 1) and (0, −14).

Answer: 3

  1. gradient = rise ÷ run = (−14 − 1) ÷ (0 − 5)
  2. = −15 ÷ −5 = 3
5.For the line y = x − 1, write the gradient and the y-intercept.

Answer: gradient 1; 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.

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

Answer: gradient −4; 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.

7.Find the gradient of the line through (−6, −4) and (−8, 0).

Answer: −2

  1. gradient = rise ÷ run = (0 − (−4)) ÷ (−8 − (−6))
  2. = 4 ÷ −2 = −2
8.Find the gradient of the line through (4, 2) and (7, 11).

Answer: 3

  1. gradient = rise ÷ run = (11 − 2) ÷ (7 − 4)
  2. = 9 ÷ 3 = 3
9.Find the gradient of the line through (6, 1) and (3, 10).

Answer: −3

  1. gradient = rise ÷ run = (10 − 1) ÷ (3 − 6)
  2. = 9 ÷ −3 = −3
10.Find the gradient of the line through (−6, −5) and (−2, −1).

Answer: 1

  1. gradient = rise ÷ run = (−1 − (−5)) ÷ (−2 − (−6))
  2. = 4 ÷ 4 = 1
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