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Year 8 Gradient and Linear Equations Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 8 linear relationships & graphs worksheet.

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

Answer: gradient 1; 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.

2.A line has a gradient of −5 and passes through (−2, 3). Find its equation.

Answer: y = −5x − 7

  1. y = −5x + (y-intercept)
  2. 3 = −5 × (−2) + (y-intercept)
  3. y-intercept = 3 − 10 = −7
  4. y = −5x − 7
3.Does the point (−5, −15) lie on the line y = 4x + 5?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = −5: y = 4 × (−5) + 5 = −15, which matches.

4.Does the point (2, 0) lie on the line y = 3x − 6?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = 2: y = 3 × 2 − 6 = 0, which matches.

5.Does the point (−2, −4) lie on the line y = 5x + 9?
  1. AYes
  2. BNo

Answer: No

Substitute x = −2: y = 5 × (−2) + 9 = −1, not −4.

6.Does the point (−3, 6) lie on the line y = −2x + 3?
  1. AYes
  2. BNo

Answer: No

Substitute x = −3: y = −2 × (−3) + 3 = 9, not 6.

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

Answer: Yes

Substitute x = 3: y = 3 × 3 + 0 = 9, which matches.

8.For the line y = −6x − 1, write the gradient and the y-intercept.

Answer: gradient −6; 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.

9.For the line y = −6x − 7, write the gradient and the y-intercept.

Answer: gradient −6; 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.

10.Does the point (−3, −6) lie on the line y = 4x + 6?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = −3: y = 4 × (−3) + 6 = −6, which matches.

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