Year 10 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 2 — 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 2 — 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 −1 and passes through (−4, −1). Find its equation.
Answer: y = −x − 5
- y = −1x + (y-intercept)
- −1 = −1 × (−4) + (y-intercept)
- y-intercept = −1 − 4 = −5
- y = −x − 5
2.Does the point (0, 5) lie on the line y = −2x + 5?
- AYes
- BNo
Answer: Yes
Substitute x = 0: y = −2 × 0 + 5 = 5, which matches.
3.Does the point (2, −3) lie on the line y = x − 5?
- AYes
- BNo
Answer: Yes
Substitute x = 2: y = 1 × 2 − 5 = −3, which matches.
4.A line has a gradient of 4 and passes through (0, −4). Find its equation.
Answer: y = 4x − 4
- y = 4x + (y-intercept)
- −4 = 4 × 0 + (y-intercept)
- y-intercept = −4 − 0 = −4
- y = 4x − 4
5.Does the point (−5, −27) lie on the line y = 5x?
- AYes
- BNo
Answer: No
Substitute x = −5: y = 5 × (−5) + 0 = −25, not −27.
6.Does the point (2, 15) lie on the line y = 5x + 5?
- AYes
- BNo
Answer: Yes
Substitute x = 2: y = 5 × 2 + 5 = 15, which matches.
7.A line has a gradient of 4 and passes through (−3, −5). Find its equation.
Answer: y = 4x + 7
- y = 4x + (y-intercept)
- −5 = 4 × (−3) + (y-intercept)
- y-intercept = −5 − (−12) = 7
- y = 4x + 7
8.For the line y = −4x − 8, write the gradient and the y-intercept.
Answer: gradient −4; y-intercept −8
In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.
9.A line has a gradient of 4 and passes through (3, 8). Find its equation.
Answer: y = 4x − 4
- y = 4x + (y-intercept)
- 8 = 4 × 3 + (y-intercept)
- y-intercept = 8 − 12 = −4
- y = 4x − 4
10.A line has a gradient of 1 and passes through (3, −2). Find its equation.
Answer: y = x − 5
- y = 1x + (y-intercept)
- −2 = 1 × 3 + (y-intercept)
- y-intercept = −2 − 3 = −5
- y = x − 5
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.