Year 10 Gradient and Linear Equations Worksheet — Level 2 — 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 2 — 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.Find the gradient of the line through (3, 4) and (4, 12).
Answer: 8
- gradient = rise ÷ run = (12 − 4) ÷ (4 − 3)
- = 8 ÷ 1 = 8
2.Find the gradient of the line through (2, 5) and (−3, 3).
Answer:
- gradient = rise ÷ run = (3 − 5) ÷ (−3 − 2)
- = −2 ÷ −5 =
3.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.
4.Find the gradient of the line through (−1, 6) and (−3, 7).
Answer: −
- gradient = rise ÷ run = (7 − 6) ÷ (−3 − (−1))
- = 1 ÷ −2 = −
5.Find the gradient of the line through (0, −4) and (−3, 1).
Answer: −
- gradient = rise ÷ run = (1 − (−4)) ÷ (−3 − 0)
- = 5 ÷ −3 = −
6.Find the gradient of the line through (1, −1) and (−2, −2).
Answer:
- gradient = rise ÷ run = (−2 − (−1)) ÷ (−2 − 1)
- = −1 ÷ −3 =
7.Find the gradient of the line through (4, −3) and (3, 3).
Answer: −6
- gradient = rise ÷ run = (3 − (−3)) ÷ (3 − 4)
- = 6 ÷ −1 = −6
8.For the line y = −6x − 9, write the gradient and the y-intercept.
Answer: gradient −6; y-intercept −9
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 −5 and passes through (1, −3). Find its equation.
Answer: y = −5x + 2
- y = −5x + (y-intercept)
- −3 = −5 × 1 + (y-intercept)
- y-intercept = −3 − (−5) = 2
- y = −5x + 2
10.Find the gradient of the line through (0, 5) and (−2, −1).
Answer: 3
- gradient = rise ÷ run = (−1 − 5) ÷ (−2 − 0)
- = −6 ÷ −2 = 3
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.