Year 8 Gradient and Linear Equations Worksheet — Level 1 — 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 1 — 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 (−1, 6) and (4, 11).
Answer: 1
- gradient = rise ÷ run = (11 − 6) ÷ (4 − (−1))
- = 5 ÷ 5 = 1
2.Find the gradient of the line through (0, 1) and (5, 11).
Answer: 2
- gradient = rise ÷ run = (11 − 1) ÷ (5 − 0)
- = 10 ÷ 5 = 2
3.For the line y = −6x − 5, write the gradient and the y-intercept.
Answer: gradient −6; 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.Find the gradient of the line through (3, −4) and (−1, −16).
Answer: 3
- gradient = rise ÷ run = (−16 − (−4)) ÷ (−1 − 3)
- = −12 ÷ −4 = 3
5.Find the gradient of the line through (−3, 6) and (0, 9).
Answer: 1
- gradient = rise ÷ run = (9 − 6) ÷ (0 − (−3))
- = 3 ÷ 3 = 1
6.Find the gradient of the line through (−1, −2) and (−5, −6).
Answer: 1
- gradient = rise ÷ run = (−6 − (−2)) ÷ (−5 − (−1))
- = −4 ÷ −4 = 1
7.Find the gradient of the line through (1, 3) and (4, 9).
Answer: 2
- gradient = rise ÷ run = (9 − 3) ÷ (4 − 1)
- = 6 ÷ 3 = 2
8.Find the gradient of the line through (5, −1) and (8, 2).
Answer: 1
- gradient = rise ÷ run = (2 − (−1)) ÷ (8 − 5)
- = 3 ÷ 3 = 1
9.For the line y = x + 7, write the gradient and the y-intercept.
Answer: gradient 1; y-intercept 7
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, −2) and (−1, −6).
Answer: −2
- gradient = rise ÷ run = (−6 − (−2)) ÷ (−1 − (−3))
- = −4 ÷ 2 = −2
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