Success TutoringWorksheets

Year 8 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 8 linear relationships & graphs worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Linear Relationships & Graphs

Year 8 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.Does the point (−5, 23) lie on the line y = −4x + 3?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = −5: y = −4 × (−5) + 3 = 23, which matches.

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

Answer: y = x − 6

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

Answer: gradient −1; 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.

4.A line has a gradient of 3 and passes through (−3, −11). Find its equation.

Answer: y = 3x − 2

  1. y = 3x + (y-intercept)
  2. −11 = 3 × (−3) + (y-intercept)
  3. y-intercept = −11 − (−9) = −2
  4. y = 3x − 2
5.Does the point (3, 17) lie on the line y = 2x + 8?
  1. AYes
  2. BNo

Answer: No

Substitute x = 3: y = 2 × 3 + 8 = 14, not 17.

6.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.

7.For the line y = −4x + 3, write the gradient and the y-intercept.

Answer: gradient −4; 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.

8.A line has a gradient of −2 and passes through (0, −4). Find its equation.

Answer: y = −2x − 4

  1. y = −2x + (y-intercept)
  2. −4 = −2 × 0 + (y-intercept)
  3. y-intercept = −4 − 0 = −4
  4. y = −2x − 4
9.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
10.A line has a gradient of 2 and passes through (2, 11). Find its equation.

Answer: y = 2x + 7

  1. y = 2x + (y-intercept)
  2. 11 = 2 × 2 + (y-intercept)
  3. y-intercept = 11 − 4 = 7
  4. y = 2x + 7
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.