Year 9 Gradient and Linear Equations Worksheet — Level 1 — Practice Set 3 — 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 1 — 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 (5, 1) and (3, 7).
Answer: −3
- gradient = rise ÷ run = (7 − 1) ÷ (3 − 5)
- = 6 ÷ −2 = −3
2.Find the gradient of the line through (6, −3) and (11, 7).
Answer: 2
- gradient = rise ÷ run = (7 − (−3)) ÷ (11 − 6)
- = 10 ÷ 5 = 2
3.For the line y = 6x − 8, write the gradient and the y-intercept.
Answer: gradient 6; 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.
4.Find the gradient of the line through (−1, −5) and (−2, −7).
Answer: 2
- gradient = rise ÷ run = (−7 − (−5)) ÷ (−2 − (−1))
- = −2 ÷ −1 = 2
5.For the line y = 3x − 4, write the gradient and the y-intercept.
Answer: gradient 3; y-intercept −4
In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.
6.Find the gradient of the line through (−3, 6) and (−5, 8).
Answer: −1
- gradient = rise ÷ run = (8 − 6) ÷ (−5 − (−3))
- = 2 ÷ −2 = −1
7.Find the gradient of the line through (−3, 5) and (−5, 9).
Answer: −2
- gradient = rise ÷ run = (9 − 5) ÷ (−5 − (−3))
- = 4 ÷ −2 = −2
8.Find the gradient of the line through (5, −3) and (10, 2).
Answer: 1
- gradient = rise ÷ run = (2 − (−3)) ÷ (10 − 5)
- = 5 ÷ 5 = 1
9.Find the gradient of the line through (1, 3) and (0, 5).
Answer: −2
- gradient = rise ÷ run = (5 − 3) ÷ (0 − 1)
- = 2 ÷ −1 = −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.