Year 10 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 10 linear relationships & graphs worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Linear Relationships & GraphsYear 10 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 4 — 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 3 and passes through (4, 20). Find its equation.
Answer: y = 3x + 8
- y = 3x + (y-intercept)
- 20 = 3 × 4 + (y-intercept)
- y-intercept = 20 − 12 = 8
- y = 3x + 8
2.Find the gradient of the line through (−6, 0) and (−11, 9).
Answer: −
- gradient = rise ÷ run = (9 − 0) ÷ (−11 − (−6))
- = 9 ÷ −5 = −
3.For the line y = −2x + 1, write the gradient and the y-intercept.
Answer: gradient −2; y-intercept 1
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 (−4, −5) and (0, −10).
Answer: −
- gradient = rise ÷ run = (−10 − (−5)) ÷ (0 − (−4))
- = −5 ÷ 4 = −
5.A line has a gradient of 4 and passes through (−2, −4). Find its equation.
Answer: y = 4x + 4
- y = 4x + (y-intercept)
- −4 = 4 × (−2) + (y-intercept)
- y-intercept = −4 − (−8) = 4
- y = 4x + 4
6.A line has a gradient of 2 and passes through (−4, −14). Find its equation.
Answer: y = 2x − 6
- y = 2x + (y-intercept)
- −14 = 2 × (−4) + (y-intercept)
- y-intercept = −14 − (−8) = −6
- y = 2x − 6
7.A line has a gradient of 5 and passes through (2, 8). Find its equation.
Answer: y = 5x − 2
- y = 5x + (y-intercept)
- 8 = 5 × 2 + (y-intercept)
- y-intercept = 8 − 10 = −2
- y = 5x − 2
8.For the line y = 5x + 2, write the gradient and the y-intercept.
Answer: gradient 5; y-intercept 2
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 (−4, 2) and (0, −6).
Answer: −2
- gradient = rise ÷ run = (−6 − 2) ÷ (0 − (−4))
- = −8 ÷ 4 = −2
10.Find the gradient of the line through (−6, 2) and (−7, 5).
Answer: −3
- gradient = rise ÷ run = (5 − 2) ÷ (−7 − (−6))
- = 3 ÷ −1 = −3
Marking tips
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