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Year 10 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 10 linear relationships & graphs worksheet.

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Year 10 Gradient and Linear Equations Worksheet — Level 3 — 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.Does the point (−2, 1) lie on the line y = 4x + 9?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = −2: y = 4 × (−2) + 9 = 1, which matches.

2.A line has a gradient of −2 and passes through (−1, 7). Find its equation.

Answer: y = −2x + 5

  1. y = −2x + (y-intercept)
  2. 7 = −2 × (−1) + (y-intercept)
  3. y-intercept = 7 − 2 = 5
  4. y = −2x + 5
3.Does the point (1, 4) lie on the line y = −3x + 8?
  1. AYes
  2. BNo

Answer: No

Substitute x = 1: y = −3 × 1 + 8 = 5, not 4.

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

Answer: y = 2x + 7

  1. y = 2x + (y-intercept)
  2. 1 = 2 × (−3) + (y-intercept)
  3. y-intercept = 1 − (−6) = 7
  4. y = 2x + 7
5.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.

6.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.

7.A line has a gradient of −3 and passes through (3, −9). Find its equation.

Answer: y = −3x

  1. y = −3x + (y-intercept)
  2. −9 = −3 × 3 + (y-intercept)
  3. y-intercept = −9 − (−9) = 0
  4. y = −3x
8.For the line y = −2x − 8, write the gradient and the y-intercept.

Answer: gradient −2; y-intercept −8

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.A line has a gradient of −4 and passes through (−2, 14). Find its equation.

Answer: y = −4x + 6

  1. y = −4x + (y-intercept)
  2. 14 = −4 × (−2) + (y-intercept)
  3. y-intercept = 14 − 8 = 6
  4. y = −4x + 6
10.Does the point (1, 7) lie on the line y = −x + 8?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = 1: y = −1 × 1 + 8 = 7, which matches.

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