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Year 9 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 2 — Answers

Answer sheet with worked solutions for the Year 9 linear relationships & graphs worksheet.

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Year 9 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 2 — 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 (−1, 0) lie on the line y = x + 1?
  1. AYes
  2. BNo

Answer: Yes

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

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

Answer: y = 2x + 2

  1. y = 2x + (y-intercept)
  2. −4 = 2 × (−3) + (y-intercept)
  3. y-intercept = −4 − (−6) = 2
  4. y = 2x + 2
3.A line has a gradient of −2 and passes through (2, −7). Find its equation.

Answer: y = −2x − 3

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

Answer: No

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

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

Answer: y = x + 5

  1. y = 1x + (y-intercept)
  2. 8 = 1 × 3 + (y-intercept)
  3. y-intercept = 8 − 3 = 5
  4. y = x + 5
6.A line has a gradient of 5 and passes through (−3, −14). Find its equation.

Answer: y = 5x + 1

  1. y = 5x + (y-intercept)
  2. −14 = 5 × (−3) + (y-intercept)
  3. y-intercept = −14 − (−15) = 1
  4. y = 5x + 1
7.Does the point (4, −15) lie on the line y = −2x − 7?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = 4: y = −2 × 4 − 7 = −15, which matches.

8.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.

9.For the line y = 4x + 1, write the gradient and the y-intercept.

Answer: gradient 4; 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.

10.A line has a gradient of −4 and passes through (−4, 13). Find its equation.

Answer: y = −4x − 3

  1. y = −4x + (y-intercept)
  2. 13 = −4 × (−4) + (y-intercept)
  3. y-intercept = 13 − 16 = −3
  4. y = −4x − 3
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