Year 10 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 3 — 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 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, 11) lie on the line y = −2x + 5?
- AYes
- BNo
Answer: No
Substitute x = −2: y = −2 × (−2) + 5 = 9, not 11.
2.A line has a gradient of −1 and passes through (0, 3). Find its equation.
Answer: y = −x + 3
- y = −1x + (y-intercept)
- 3 = −1 × 0 + (y-intercept)
- y-intercept = 3 − 0 = 3
- y = −x + 3
3.Does the point (5, −15) lie on the line y = −5x + 7?
- AYes
- BNo
Answer: No
Substitute x = 5: y = −5 × 5 + 7 = −18, not −15.
4.Does the point (−2, −3) lie on the line y = 3x + 3?
- AYes
- BNo
Answer: Yes
Substitute x = −2: y = 3 × (−2) + 3 = −3, which matches.
5.A line has a gradient of 1 and passes through (−1, −2). Find its equation.
Answer: y = x − 1
- y = 1x + (y-intercept)
- −2 = 1 × (−1) + (y-intercept)
- y-intercept = −2 − (−1) = −1
- y = x − 1
6.A line has a gradient of −2 and passes through (−3, 15). Find its equation.
Answer: y = −2x + 9
- y = −2x + (y-intercept)
- 15 = −2 × (−3) + (y-intercept)
- y-intercept = 15 − 6 = 9
- y = −2x + 9
7.A line has a gradient of 3 and passes through (3, 4). Find its equation.
Answer: y = 3x − 5
- y = 3x + (y-intercept)
- 4 = 3 × 3 + (y-intercept)
- y-intercept = 4 − 9 = −5
- y = 3x − 5
8.A line has a gradient of −3 and passes through (3, −6). Find its equation.
Answer: y = −3x + 3
- y = −3x + (y-intercept)
- −6 = −3 × 3 + (y-intercept)
- y-intercept = −6 − (−9) = 3
- y = −3x + 3
9.A line has a gradient of −5 and passes through (−1, 4). Find its equation.
Answer: y = −5x − 1
- y = −5x + (y-intercept)
- 4 = −5 × (−1) + (y-intercept)
- y-intercept = 4 − 5 = −1
- y = −5x − 1
10.For the line y = −2x − 3, write the gradient and the y-intercept.
Answer: gradient −2; 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.