Year 8 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 2 — 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 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 2 and passes through (2, 11). Find its equation.
Answer: y = 2x + 7
- y = 2x + (y-intercept)
- 11 = 2 × 2 + (y-intercept)
- y-intercept = 11 − 4 = 7
- y = 2x + 7
2.A line has a gradient of 4 and passes through (−3, −7). Find its equation.
Answer: y = 4x + 5
- y = 4x + (y-intercept)
- −7 = 4 × (−3) + (y-intercept)
- y-intercept = −7 − (−12) = 5
- y = 4x + 5
3.A line has a gradient of −3 and passes through (−1, −5). Find its equation.
Answer: y = −3x − 8
- y = −3x + (y-intercept)
- −5 = −3 × (−1) + (y-intercept)
- y-intercept = −5 − 3 = −8
- y = −3x − 8
4.For the line y = −4x, write the gradient and the y-intercept.
Answer: gradient −4; 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.
5.Find the gradient of the line through (0, −2) and (−3, 0).
Answer: −
- gradient = rise ÷ run = (0 − (−2)) ÷ (−3 − 0)
- = 2 ÷ −3 = −
6.A line has a gradient of −5 and passes through (−4, 21). Find its equation.
Answer: y = −5x + 1
- y = −5x + (y-intercept)
- 21 = −5 × (−4) + (y-intercept)
- y-intercept = 21 − 20 = 1
- y = −5x + 1
7.Find the gradient of the line through (−5, 0) and (−3, 9).
Answer:
- gradient = rise ÷ run = (9 − 0) ÷ (−3 − (−5))
- = 9 ÷ 2 =
8.For the line y = 3x + 9, write the gradient and the y-intercept.
Answer: gradient 3; y-intercept 9
In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.
9.Find the gradient of the line through (−3, 4) and (−1, 6).
Answer: 1
- gradient = rise ÷ run = (6 − 4) ÷ (−1 − (−3))
- = 2 ÷ 2 = 1
10.Find the gradient of the line through (0, 2) and (−2, 10).
Answer: −4
- gradient = rise ÷ run = (10 − 2) ÷ (−2 − 0)
- = 8 ÷ −2 = −4
Marking tips
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