Year 9 Gradient and Linear Equations Worksheet — Level 1 — 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 — Answers
Show your working. Gradient = rise ÷ run; the equation of a line can be written as y = (gradient)x + (y-intercept).
1.For the line y = −6x + 4, write the gradient and the y-intercept.
Answer: gradient −6; 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.
2.Find the gradient of the line through (5, 4) and (6, 6).
Answer: 2
- gradient = rise ÷ run = (6 − 4) ÷ (6 − 5)
- = 2 ÷ 1 = 2
3.Find the gradient of the line through (0, −4) and (−1, −2).
Answer: −2
- gradient = rise ÷ run = (−2 − (−4)) ÷ (−1 − 0)
- = 2 ÷ −1 = −2
4.Find the gradient of the line through (4, −6) and (−1, −21).
Answer: 3
- gradient = rise ÷ run = (−21 − (−6)) ÷ (−1 − 4)
- = −15 ÷ −5 = 3
5.Find the gradient of the line through (5, −3) and (4, 0).
Answer: −3
- gradient = rise ÷ run = (0 − (−3)) ÷ (4 − 5)
- = 3 ÷ −1 = −3
6.Find the gradient of the line through (−3, 2) and (−8, 7).
Answer: −1
- gradient = rise ÷ run = (7 − 2) ÷ (−8 − (−3))
- = 5 ÷ −5 = −1
7.Find the gradient of the line through (4, −5) and (6, −1).
Answer: 2
- gradient = rise ÷ run = (−1 − (−5)) ÷ (6 − 4)
- = 4 ÷ 2 = 2
8.Find the gradient of the line through (−5, −4) and (−9, −12).
Answer: 2
- gradient = rise ÷ run = (−12 − (−4)) ÷ (−9 − (−5))
- = −8 ÷ −4 = 2
9.For the line y = 2x + 5, write the gradient and the y-intercept.
Answer: gradient 2; 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.
10.Find the gradient of the line through (3, 4) and (1, 6).
Answer: −1
- gradient = rise ÷ run = (6 − 4) ÷ (1 − 3)
- = 2 ÷ −2 = −1
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.