Year 11 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 linear relationships & graphs worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Linear Relationships & GraphsYear 11 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 3 — 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 (5, 6) and (9, −1).
Answer: −
- gradient = rise ÷ run = (−1 − 6) ÷ (9 − 5)
- = −7 ÷ 4 = −
2.Find the gradient of the line through (−2, 2) and (−7, 11).
Answer: −
- gradient = rise ÷ run = (11 − 2) ÷ (−7 − (−2))
- = 9 ÷ −5 = −
3.A line has a gradient of −1 and passes through (4, −13). Find its equation.
Answer: y = −x − 9
- y = −1x + (y-intercept)
- −13 = −1 × 4 + (y-intercept)
- y-intercept = −13 − (−4) = −9
- y = −x − 9
4.Find the gradient of the line through (6, 0) and (7, −3).
Answer: −3
- gradient = rise ÷ run = (−3 − 0) ÷ (7 − 6)
- = −3 ÷ 1 = −3
5.For the line y = −x + 6, write the gradient and the y-intercept.
Answer: gradient −1; y-intercept 6
In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.
6.A line has a gradient of 3 and passes through (4, 18). Find its equation.
Answer: y = 3x + 6
- y = 3x + (y-intercept)
- 18 = 3 × 4 + (y-intercept)
- y-intercept = 18 − 12 = 6
- y = 3x + 6
7.A line has a gradient of 5 and passes through (2, 14). Find its equation.
Answer: y = 5x + 4
- y = 5x + (y-intercept)
- 14 = 5 × 2 + (y-intercept)
- y-intercept = 14 − 10 = 4
- y = 5x + 4
8.Find the gradient of the line through (−3, −6) and (−4, −11).
Answer: 5
- gradient = rise ÷ run = (−11 − (−6)) ÷ (−4 − (−3))
- = −5 ÷ −1 = 5
9.Find the gradient of the line through (6, −4) and (10, −3).
Answer:
- gradient = rise ÷ run = (−3 − (−4)) ÷ (10 − 6)
- = 1 ÷ 4 =
10.Find the gradient of the line through (6, −6) and (1, −15).
Answer:
- gradient = rise ÷ run = (−15 − (−6)) ÷ (1 − 6)
- = −9 ÷ −5 =
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