Year 10 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 10 linear relationships & graphs worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Linear Relationships & GraphsYear 10 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).
Answer: y = 4x + 8
- y = 4x + (y-intercept)
- 4 = 4 × (−1) + (y-intercept)
- y-intercept = 4 − (−4) = 8
- y = 4x + 8
Answer: gradient 5; 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.
Answer: y = x + 6
- y = 1x + (y-intercept)
- 9 = 1 × 3 + (y-intercept)
- y-intercept = 9 − 3 = 6
- y = x + 6
- AYes
- BNo
Answer: Yes
Substitute x = −4: y = −4 × (−4) − 3 = 13, which matches.
- AYes
- BNo
Answer: Yes
Substitute x = −4: y = −4 × (−4) − 5 = 11, which matches.
Answer: gradient 5; 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 = 2 × 2 + 4 = 8, not 7.
Answer: y = −3x − 3
- y = −3x + (y-intercept)
- −9 = −3 × 2 + (y-intercept)
- y-intercept = −9 − (−6) = −3
- y = −3x − 3
Answer: gradient −6; y-intercept 0
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: 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.
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.