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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.A line has a gradient of 4 and passes through (−2, −10). Find its equation.

Answer: y = 4x − 2

  1. y = 4x + (y-intercept)
  2. −10 = 4 × (−2) + (y-intercept)
  3. y-intercept = −10 − (−8) = −2
  4. y = 4x − 2
2.A line has a gradient of −3 and passes through (−4, 14). Find its equation.

Answer: y = −3x + 2

  1. y = −3x + (y-intercept)
  2. 14 = −3 × (−4) + (y-intercept)
  3. y-intercept = 14 − 12 = 2
  4. y = −3x + 2
3.Does the point (2, 5) lie on the line y = 3x − 1?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = 2: y = 3 × 2 − 1 = 5, which matches.

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

Answer: y = −4x + 3

  1. y = −4x + (y-intercept)
  2. 19 = −4 × (−4) + (y-intercept)
  3. y-intercept = 19 − 16 = 3
  4. y = −4x + 3
5.For the line y = −2x + 5, write the gradient and the y-intercept.

Answer: gradient −2; y-intercept 5

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

Answer: gradient −6; 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.A line has a gradient of −1 and passes through (−2, 3). Find its equation.

Answer: y = −x + 1

  1. y = −1x + (y-intercept)
  2. 3 = −1 × (−2) + (y-intercept)
  3. y-intercept = 3 − 2 = 1
  4. y = −x + 1
8.A line has a gradient of 2 and passes through (4, 15). Find its equation.

Answer: y = 2x + 7

  1. y = 2x + (y-intercept)
  2. 15 = 2 × 4 + (y-intercept)
  3. y-intercept = 15 − 8 = 7
  4. y = 2x + 7
9.Does the point (−1, 3) lie on the line y = −5x − 2?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = −1: y = −5 × (−1) − 2 = 3, which matches.

10.Does the point (3, 0) lie on the line y = −2x + 8?
  1. AYes
  2. BNo

Answer: No

Substitute x = 3: y = −2 × 3 + 8 = 2, not 0.

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