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Year 9 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 4 — 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 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 + 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.

2.A line has a gradient of 2 and passes through (0, −5). Find its equation.

Answer: y = 2x − 5

  1. y = 2x + (y-intercept)
  2. −5 = 2 × 0 + (y-intercept)
  3. y-intercept = −5 − 0 = −5
  4. y = 2x − 5
3.A line has a gradient of −2 and passes through (−4, 16). Find its equation.

Answer: y = −2x + 8

  1. y = −2x + (y-intercept)
  2. 16 = −2 × (−4) + (y-intercept)
  3. y-intercept = 16 − 8 = 8
  4. y = −2x + 8
4.For the line y = 4x − 4, write the gradient and the y-intercept.

Answer: gradient 4; y-intercept −4

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

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

Answer: gradient −4; 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.A line has a gradient of 4 and passes through (−1, −7). Find its equation.

Answer: y = 4x − 3

  1. y = 4x + (y-intercept)
  2. −7 = 4 × (−1) + (y-intercept)
  3. y-intercept = −7 − (−4) = −3
  4. y = 4x − 3
7.A line has a gradient of −5 and passes through (−3, 15). Find its equation.

Answer: y = −5x

  1. y = −5x + (y-intercept)
  2. 15 = −5 × (−3) + (y-intercept)
  3. y-intercept = 15 − 15 = 0
  4. y = −5x
8.A line has a gradient of 5 and passes through (4, 28). Find its equation.

Answer: y = 5x + 8

  1. y = 5x + (y-intercept)
  2. 28 = 5 × 4 + (y-intercept)
  3. y-intercept = 28 − 20 = 8
  4. y = 5x + 8
9.A line has a gradient of 3 and passes through (−3, 0). Find its equation.

Answer: y = 3x + 9

  1. y = 3x + (y-intercept)
  2. 0 = 3 × (−3) + (y-intercept)
  3. y-intercept = 0 − (−9) = 9
  4. y = 3x + 9
10.A line has a gradient of −3 and passes through (−2, 8). Find its equation.

Answer: y = −3x + 2

  1. y = −3x + (y-intercept)
  2. 8 = −3 × (−2) + (y-intercept)
  3. y-intercept = 8 − 6 = 2
  4. y = −3x + 2
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