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Year 9 Gradient and Linear Equations Worksheet — Level 2 — 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 2 — 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.A line has a gradient of −4 and passes through (2, −8). Find its equation.

Answer: y = −4x

  1. y = −4x + (y-intercept)
  2. −8 = −4 × 2 + (y-intercept)
  3. y-intercept = −8 − (−8) = 0
  4. y = −4x
2.A line has a gradient of −3 and passes through (2, −11). Find its equation.

Answer: y = −3x − 5

  1. y = −3x + (y-intercept)
  2. −11 = −3 × 2 + (y-intercept)
  3. y-intercept = −11 − (−6) = −5
  4. y = −3x − 5
3.A line has a gradient of 2 and passes through (−2, 1). Find its equation.

Answer: y = 2x + 5

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

Answer: y = −5x − 9

  1. y = −5x + (y-intercept)
  2. −14 = −5 × 1 + (y-intercept)
  3. y-intercept = −14 − (−5) = −9
  4. y = −5x − 9
5.A line has a gradient of −3 and passes through (2, −2). Find its equation.

Answer: y = −3x + 4

  1. y = −3x + (y-intercept)
  2. −2 = −3 × 2 + (y-intercept)
  3. y-intercept = −2 − (−6) = 4
  4. y = −3x + 4
6.For the line y = −5x − 9, write the gradient and the y-intercept.

Answer: gradient −5; 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.

7.For the line y = −4x + 8, write the gradient and the y-intercept.

Answer: gradient −4; y-intercept 8

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.Find the gradient of the line through (−2, −4) and (2, −5).

Answer: −

  1. gradient = rise ÷ run = (−5 − (−4)) ÷ (2 − (−2))
  2. = −1 ÷ 4 = −
9.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.

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

Answer: y = 3x + 7

  1. y = 3x + (y-intercept)
  2. 4 = 3 × (−1) + (y-intercept)
  3. y-intercept = 4 − (−3) = 7
  4. y = 3x + 7
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