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