Year 9 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 9 linear relationships & graphs worksheet.
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Linear Relationships & GraphsYear 9 Gradient and Linear Equations Worksheet — Level 2 — 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, 4). Find its equation.
Answer: y = −x + 8
- y = −1x + (y-intercept)
- 4 = −1 × 4 + (y-intercept)
- y-intercept = 4 − (−4) = 8
- y = −x + 8
2.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
3.For the line y = −4x − 5, write the gradient and the y-intercept.
Answer: gradient −4; 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.
4.A line has a gradient of −4 and passes through (4, −19). Find its equation.
Answer: y = −4x − 3
- y = −4x + (y-intercept)
- −19 = −4 × 4 + (y-intercept)
- y-intercept = −19 − (−16) = −3
- y = −4x − 3
5.Find the gradient of the line through (5, 2) and (8, 5).
Answer: 1
- gradient = rise ÷ run = (5 − 2) ÷ (8 − 5)
- = 3 ÷ 3 = 1
6.Find the gradient of the line through (1, −3) and (−1, −5).
Answer: 1
- gradient = rise ÷ run = (−5 − (−3)) ÷ (−1 − 1)
- = −2 ÷ −2 = 1
7.Find the gradient of the line through (2, 0) and (−2, 2).
Answer: −
- gradient = rise ÷ run = (2 − 0) ÷ (−2 − 2)
- = 2 ÷ −4 = −
8.A line has a gradient of 5 and passes through (0, 2). Find its equation.
Answer: y = 5x + 2
- y = 5x + (y-intercept)
- 2 = 5 × 0 + (y-intercept)
- y-intercept = 2 − 0 = 2
- y = 5x + 2
9.A line has a gradient of −5 and passes through (−4, 26). Find its equation.
Answer: y = −5x + 6
- y = −5x + (y-intercept)
- 26 = −5 × (−4) + (y-intercept)
- y-intercept = 26 − 20 = 6
- y = −5x + 6
10.Find the gradient of the line through (−5, −3) and (−7, −7).
Answer: 2
- gradient = rise ÷ run = (−7 − (−3)) ÷ (−7 − (−5))
- = −4 ÷ −2 = 2
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.
Great work. Here's what to try next: