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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 4 and passes through (2, 3). Find its equation.

Answer: y = 4x − 5

  1. y = 4x + (y-intercept)
  2. 3 = 4 × 2 + (y-intercept)
  3. y-intercept = 3 − 8 = −5
  4. y = 4x − 5
2.Does the point (3, 14) lie on the line y = 2x + 8?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = 3: y = 2 × 3 + 8 = 14, which matches.

3.Does the point (−5, 22) lie on the line y = −3x + 9?
  1. AYes
  2. BNo

Answer: No

Substitute x = −5: y = −3 × (−5) + 9 = 24, not 22.

4.Does the point (5, 13) lie on the line y = 2x + 3?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = 5: y = 2 × 5 + 3 = 13, which matches.

5.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
6.For the line y = −5x − 3, write the gradient and the y-intercept.

Answer: gradient −5; 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.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.

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

Answer: y = 2x

  1. y = 2x + (y-intercept)
  2. 2 = 2 × 1 + (y-intercept)
  3. y-intercept = 2 − 2 = 0
  4. y = 2x
9.For the line y = −5x − 4, write the gradient and the y-intercept.

Answer: gradient −5; 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.

10.Does the point (−2, −4) lie on the line y = −x − 3?
  1. AYes
  2. BNo

Answer: No

Substitute x = −2: y = −1 × (−2) − 3 = −1, not −4.

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