Year 8 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 4 — 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 2 — Practice Set 4 — 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 (6, 6) and (4, −3).
Answer:
- gradient = rise ÷ run = (−3 − 6) ÷ (4 − 6)
- = −9 ÷ −2 =
2.Find the gradient of the line through (6, −2) and (5, −6).
Answer: 4
- gradient = rise ÷ run = (−6 − (−2)) ÷ (5 − 6)
- = −4 ÷ −1 = 4
3.A line has a gradient of −1 and passes through (−2, 8). Find its equation.
Answer: y = −x + 6
- y = −1x + (y-intercept)
- 8 = −1 × (−2) + (y-intercept)
- y-intercept = 8 − 2 = 6
- y = −x + 6
4.Find the gradient of the line through (−3, 1) and (1, 0).
Answer: −
- gradient = rise ÷ run = (0 − 1) ÷ (1 − (−3))
- = −1 ÷ 4 = −
5.Find the gradient of the line through (1, 6) and (4, 13).
Answer:
- gradient = rise ÷ run = (13 − 6) ÷ (4 − 1)
- = 7 ÷ 3 =
6.For the line y = −6x, write the gradient and the y-intercept.
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.
7.For the line y = −4x + 2, write the gradient and the y-intercept.
Answer: gradient −4; 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.
8.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
9.Find the gradient of the line through (−2, −1) and (1, 7).
Answer:
- gradient = rise ÷ run = (7 − (−1)) ÷ (1 − (−2))
- = 8 ÷ 3 =
10.A line has a gradient of 5 and passes through (−2, −10). Find its equation.
Answer: y = 5x
- y = 5x + (y-intercept)
- −10 = 5 × (−2) + (y-intercept)
- y-intercept = −10 − (−10) = 0
- y = 5x
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.
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