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Year 10 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 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 — Practice Set 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 = 3x, write the gradient and the y-intercept.

Answer: gradient 3; 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.

2.A line has a gradient of 5 and passes through (−4, −21). Find its equation.

Answer: y = 5x − 1

  1. y = 5x + (y-intercept)
  2. −21 = 5 × (−4) + (y-intercept)
  3. y-intercept = −21 − (−20) = −1
  4. y = 5x − 1
3.Does the point (−5, −7) lie on the line y = 2x + 3?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = −5: y = 2 × (−5) + 3 = −7, which matches.

4.Does the point (−4, 15) lie on the line y = −2x + 9?
  1. AYes
  2. BNo

Answer: No

Substitute x = −4: y = −2 × (−4) + 9 = 17, not 15.

5.A line has a gradient of 3 and passes through (0, 9). Find its equation.

Answer: y = 3x + 9

  1. y = 3x + (y-intercept)
  2. 9 = 3 × 0 + (y-intercept)
  3. y-intercept = 9 − 0 = 9
  4. y = 3x + 9
6.A line has a gradient of −3 and passes through (4, −19). Find its equation.

Answer: y = −3x − 7

  1. y = −3x + (y-intercept)
  2. −19 = −3 × 4 + (y-intercept)
  3. y-intercept = −19 − (−12) = −7
  4. y = −3x − 7
7.Does the point (−3, −11) lie on the line y = 2x − 3?
  1. AYes
  2. BNo

Answer: No

Substitute x = −3: y = 2 × (−3) − 3 = −9, not −11.

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

Answer: y = −x − 6

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

Answer: gradient −3; 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.

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

Answer: No

Substitute x = −5: y = 2 × (−5) + 1 = −9, not −6.

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