Success TutoringWorksheets

Year 9 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 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 — 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.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
2.For the line y = 4x + 2, write the gradient and the y-intercept.

Answer: gradient 4; y-intercept 2

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.Does the point (2, −9) lie on the line y = x − 8?
  1. AYes
  2. BNo

Answer: No

Substitute x = 2: y = 1 × 2 − 8 = −6, not −9.

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

Answer: gradient 6; 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.Does the point (5, 6) lie on the line y = x + 3?
  1. AYes
  2. BNo

Answer: No

Substitute x = 5: y = 1 × 5 + 3 = 8, not 6.

6.For the line y = x − 3, write the gradient and the y-intercept.

Answer: gradient 1; y-intercept −3

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.Does the point (0, −1) lie on the line y = −4x − 4?
  1. AYes
  2. BNo

Answer: No

Substitute x = 0: y = −4 × 0 − 4 = −4, not −1.

8.Does the point (4, 2) lie on the line y = −x + 7?
  1. AYes
  2. BNo

Answer: No

Substitute x = 4: y = −1 × 4 + 7 = 3, not 2.

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

Answer: Yes

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

10.For the line y = −2x − 7, write the gradient and the y-intercept.

Answer: gradient −2; 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.

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.