Success TutoringWorksheets

Year 9 Gradient and Linear Equations Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 9 linear relationships & graphs worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Linear Relationships & Graphs

Year 9 Gradient and Linear Equations Worksheet — Level 3 — Answers

Show your working. Gradient = rise ÷ run; the equation of a line can be written as y = (gradient)x + (y-intercept).

1.Does the point (−2, −12) lie on the line y = 2x − 8?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = −2: y = 2 × (−2) − 8 = −12, which matches.

2.For the line y = −6x − 1, write the gradient and the y-intercept.

Answer: gradient −6; y-intercept −1

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.A line has a gradient of 5 and passes through (3, 18). Find its equation.

Answer: y = 5x + 3

  1. y = 5x + (y-intercept)
  2. 18 = 5 × 3 + (y-intercept)
  3. y-intercept = 18 − 15 = 3
  4. y = 5x + 3
4.A line has a gradient of 4 and passes through (1, 12). Find its equation.

Answer: y = 4x + 8

  1. y = 4x + (y-intercept)
  2. 12 = 4 × 1 + (y-intercept)
  3. y-intercept = 12 − 4 = 8
  4. y = 4x + 8
5.A line has a gradient of −1 and passes through (2, −3). Find its equation.

Answer: y = −x − 1

  1. y = −1x + (y-intercept)
  2. −3 = −1 × 2 + (y-intercept)
  3. y-intercept = −3 − (−2) = −1
  4. y = −x − 1
6.A line has a gradient of −1 and passes through (−4, 13). Find its equation.

Answer: y = −x + 9

  1. y = −1x + (y-intercept)
  2. 13 = −1 × (−4) + (y-intercept)
  3. y-intercept = 13 − 4 = 9
  4. y = −x + 9
7.A line has a gradient of −5 and passes through (4, −26). Find its equation.

Answer: y = −5x − 6

  1. y = −5x + (y-intercept)
  2. −26 = −5 × 4 + (y-intercept)
  3. y-intercept = −26 − (−20) = −6
  4. y = −5x − 6
8.For the line y = x + 9, write the gradient and the y-intercept.

Answer: gradient 1; 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.

9.A line has a gradient of 5 and passes through (−3, −21). Find its equation.

Answer: y = 5x − 6

  1. y = 5x + (y-intercept)
  2. −21 = 5 × (−3) + (y-intercept)
  3. y-intercept = −21 − (−15) = −6
  4. y = 5x − 6
10.A line has a gradient of 4 and passes through (3, 12). Find its equation.

Answer: y = 4x

  1. y = 4x + (y-intercept)
  2. 12 = 4 × 3 + (y-intercept)
  3. y-intercept = 12 − 12 = 0
  4. y = 4x
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.