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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.For the line y = −4x + 5, write the gradient and the y-intercept.

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

Answer: y = −x − 5

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

Answer: No

Substitute x = 2: y = −5 × 2 + 8 = −2, not 1.

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

Answer: Yes

Substitute x = −5: y = −1 × (−5) + 4 = 9, which matches.

5.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.

6.Does the point (−3, −10) lie on the line y = 2x − 5?
  1. AYes
  2. BNo

Answer: No

Substitute x = −3: y = 2 × (−3) − 5 = −11, not −10.

7.For the line y = 4x − 6, write the gradient and the y-intercept.

Answer: gradient 4; y-intercept −6

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 − 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.

9.A line has a gradient of −1 and passes through (3, −9). Find its equation.

Answer: y = −x − 6

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

Answer: gradient −3; 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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