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Year 10 Gradient and Linear Equations Worksheet — Level 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 — 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 −2 and passes through (3, −2). Find its equation.

Answer: y = −2x + 4

  1. y = −2x + (y-intercept)
  2. −2 = −2 × 3 + (y-intercept)
  3. y-intercept = −2 − (−6) = 4
  4. y = −2x + 4
2.A line has a gradient of 2 and passes through (0, −1). Find its equation.

Answer: y = 2x − 1

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

Answer: gradient 4; 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.

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

Answer: y = 2x + 5

  1. y = 2x + (y-intercept)
  2. 3 = 2 × (−1) + (y-intercept)
  3. y-intercept = 3 − (−2) = 5
  4. y = 2x + 5
5.A line has a gradient of −2 and passes through (4, 1). Find its equation.

Answer: y = −2x + 9

  1. y = −2x + (y-intercept)
  2. 1 = −2 × 4 + (y-intercept)
  3. y-intercept = 1 − (−8) = 9
  4. y = −2x + 9
6.For the line y = −x + 7, write the gradient and the y-intercept.

Answer: gradient −1; y-intercept 7

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 + 5, write the gradient and the y-intercept.

Answer: gradient 6; 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.

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

Answer: Yes

Substitute x = 1: y = −1 × 1 + 0 = −1, which matches.

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

Answer: y = 2x + 8

  1. y = 2x + (y-intercept)
  2. 2 = 2 × (−3) + (y-intercept)
  3. y-intercept = 2 − (−6) = 8
  4. y = 2x + 8
10.For the line y = −2x + 9, write the gradient and the y-intercept.

Answer: gradient −2; y-intercept 9

In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.

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