Year 8 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 8 linear relationships & graphs worksheet.
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Linear Relationships & GraphsYear 8 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 2 — Answers
Show your working. Gradient = rise ÷ run; the equation of a line can be written as y = (gradient)x + (y-intercept).
Answer: y = −2x + 7
- y = −2x + (y-intercept)
- 11 = −2 × (−2) + (y-intercept)
- y-intercept = 11 − 4 = 7
- y = −2x + 7
Answer: gradient −4; y-intercept −6
In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.
- AYes
- BNo
Answer: No
Substitute x = −4: y = 2 × (−4) + 1 = −7, not −9.
Answer: gradient 3; 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.
Answer: y = −x + 2
- y = −1x + (y-intercept)
- 5 = −1 × (−3) + (y-intercept)
- y-intercept = 5 − 3 = 2
- y = −x + 2
Answer: gradient 6; 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.
Answer: y = x − 4
- y = 1x + (y-intercept)
- −4 = 1 × 0 + (y-intercept)
- y-intercept = −4 − 0 = −4
- y = x − 4
- AYes
- BNo
Answer: Yes
Substitute x = −1: y = 4 × (−1) − 7 = −11, which matches.
Answer: gradient 4; 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.
- AYes
- BNo
Answer: No
Substitute x = −2: y = 5 × (−2) + 5 = −5, not −8.
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.