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Year 8 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 4 — 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 — 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.For the line y = −5x + 5, write the gradient and the y-intercept.

Answer: gradient −5; 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.

2.For the line y = 2x, write the gradient and the y-intercept.

Answer: gradient 2; y-intercept 0

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

3.Does the point (3, 16) lie on the line y = 4x + 3?
  1. AYes
  2. BNo

Answer: No

Substitute x = 3: y = 4 × 3 + 3 = 15, not 16.

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

Answer: y = −3x − 5

  1. y = −3x + (y-intercept)
  2. 4 = −3 × (−3) + (y-intercept)
  3. y-intercept = 4 − 9 = −5
  4. y = −3x − 5
5.Does the point (−2, 12) lie on the line y = −5x + 4?
  1. AYes
  2. BNo

Answer: No

Substitute x = −2: y = −5 × (−2) + 4 = 14, not 12.

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

Answer: No

Substitute x = 1: y = 1 × 1 + 6 = 7, not 10.

7.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.

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

Answer: gradient 1; y-intercept 0

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.A line has a gradient of 5 and passes through (−2, −7). Find its equation.

Answer: y = 5x + 3

  1. y = 5x + (y-intercept)
  2. −7 = 5 × (−2) + (y-intercept)
  3. y-intercept = −7 − (−10) = 3
  4. y = 5x + 3
10.Does the point (4, 23) lie on the line y = 5x + 3?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = 4: y = 5 × 4 + 3 = 23, which matches.

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