Year 11 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 4 — 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 4 — 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 (−2, 5) and (1, 12).
Answer:
- gradient = rise ÷ run = (12 − 5) ÷ (1 − (−2))
- = 7 ÷ 3 =
2.Find the gradient of the line through (6, −2) and (8, −3).
Answer: −
- gradient = rise ÷ run = (−3 − (−2)) ÷ (8 − 6)
- = −1 ÷ 2 = −
3.A line has a gradient of 5 and passes through (−4, −19). Find its equation.
Answer: y = 5x + 1
- y = 5x + (y-intercept)
- −19 = 5 × (−4) + (y-intercept)
- y-intercept = −19 − (−20) = 1
- y = 5x + 1
4.Find the gradient of the line through (6, −4) and (5, −13).
Answer: 9
- gradient = rise ÷ run = (−13 − (−4)) ÷ (5 − 6)
- = −9 ÷ −1 = 9
5.Find the gradient of the line through (−4, 6) and (−7, 10).
Answer: −
- gradient = rise ÷ run = (10 − 6) ÷ (−7 − (−4))
- = 4 ÷ −3 = −
6.A line has a gradient of −4 and passes through (0, −3). Find its equation.
Answer: y = −4x − 3
- y = −4x + (y-intercept)
- −3 = −4 × 0 + (y-intercept)
- y-intercept = −3 − 0 = −3
- y = −4x − 3
7.A line has a gradient of −3 and passes through (0, −6). Find its equation.
Answer: y = −3x − 6
- y = −3x + (y-intercept)
- −6 = −3 × 0 + (y-intercept)
- y-intercept = −6 − 0 = −6
- y = −3x − 6
8.A line has a gradient of −5 and passes through (−3, 6). Find its equation.
Answer: y = −5x − 9
- y = −5x + (y-intercept)
- 6 = −5 × (−3) + (y-intercept)
- y-intercept = 6 − 15 = −9
- y = −5x − 9
9.A line has a gradient of −1 and passes through (−4, −3). Find its equation.
Answer: y = −x − 7
- y = −1x + (y-intercept)
- −3 = −1 × (−4) + (y-intercept)
- y-intercept = −3 − 4 = −7
- y = −x − 7
10.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.
Marking tips
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