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Year 10 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 4 — 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 4 — 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 = −2x − 2, write the gradient and the y-intercept.

Answer: gradient −2; y-intercept −2

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 = −2x − 4, write the gradient and the y-intercept.

Answer: gradient −2; 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.

3.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
4.For the line y = 6x − 8, write the gradient and the y-intercept.

Answer: gradient 6; 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.

5.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.

6.A line has a gradient of −3 and passes through (−4, 19). Find its equation.

Answer: y = −3x + 7

  1. y = −3x + (y-intercept)
  2. 19 = −3 × (−4) + (y-intercept)
  3. y-intercept = 19 − 12 = 7
  4. y = −3x + 7
7.For the line y = −3x − 1, write the gradient and the y-intercept.

Answer: gradient −3; 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.

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

Answer: y = −3x

  1. y = −3x + (y-intercept)
  2. −3 = −3 × 1 + (y-intercept)
  3. y-intercept = −3 − (−3) = 0
  4. y = −3x
9.Does the point (4, −4) lie on the line y = x − 7?
  1. AYes
  2. BNo

Answer: No

Substitute x = 4: y = 1 × 4 − 7 = −3, not −4.

10.Does the point (1, −7) lie on the line y = x − 7?
  1. AYes
  2. BNo

Answer: No

Substitute x = 1: y = 1 × 1 − 7 = −6, not −7.

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