Year 10 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 2 — 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 2 — 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 (−4, 3) and (−7, −6).
Answer: 3
- gradient = rise ÷ run = (−6 − 3) ÷ (−7 − (−4))
- = −9 ÷ −3 = 3
2.Find the gradient of the line through (4, 6) and (7, 7).
Answer:
- gradient = rise ÷ run = (7 − 6) ÷ (7 − 4)
- = 1 ÷ 3 =
3.Find the gradient of the line through (−2, −1) and (−5, 7).
Answer: −
- gradient = rise ÷ run = (7 − (−1)) ÷ (−5 − (−2))
- = 8 ÷ −3 = −
4.A line has a gradient of 1 and passes through (−3, 3). Find its equation.
Answer: y = x + 6
- y = 1x + (y-intercept)
- 3 = 1 × (−3) + (y-intercept)
- y-intercept = 3 − (−3) = 6
- y = x + 6
5.A line has a gradient of −5 and passes through (−3, 17). Find its equation.
Answer: y = −5x + 2
- y = −5x + (y-intercept)
- 17 = −5 × (−3) + (y-intercept)
- y-intercept = 17 − 15 = 2
- y = −5x + 2
6.For the line y = −3x − 7, write the gradient and the y-intercept.
Answer: gradient −3; 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.
7.Find the gradient of the line through (−5, −5) and (−1, 1).
Answer:
- gradient = rise ÷ run = (1 − (−5)) ÷ (−1 − (−5))
- = 6 ÷ 4 =
8.Find the gradient of the line through (5, 2) and (7, −7).
Answer: −
- gradient = rise ÷ run = (−7 − 2) ÷ (7 − 5)
- = −9 ÷ 2 = −
9.For the line y = x + 5, write the gradient and the y-intercept.
Answer: gradient 1; 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 (0, −4) and (−1, 4).
Answer: −8
- gradient = rise ÷ run = (4 − (−4)) ÷ (−1 − 0)
- = 8 ÷ −1 = −8
Marking tips
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