Year 9 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 3 — 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 — 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.A line has a gradient of 3 and passes through (1, 6). Find its equation.
Answer: y = 3x + 3
- y = 3x + (y-intercept)
- 6 = 3 × 1 + (y-intercept)
- y-intercept = 6 − 3 = 3
- y = 3x + 3
2.Find the gradient of the line through (4, −1) and (1, 3).
Answer: −
- gradient = rise ÷ run = (3 − (−1)) ÷ (1 − 4)
- = 4 ÷ −3 = −
3.A line has a gradient of −5 and passes through (0, −8). Find its equation.
Answer: y = −5x − 8
- y = −5x + (y-intercept)
- −8 = −5 × 0 + (y-intercept)
- y-intercept = −8 − 0 = −8
- y = −5x − 8
4.A line has a gradient of 3 and passes through (−1, 0). Find its equation.
Answer: y = 3x + 3
- y = 3x + (y-intercept)
- 0 = 3 × (−1) + (y-intercept)
- y-intercept = 0 − (−3) = 3
- y = 3x + 3
5.For the line y = 6x, write the gradient and the y-intercept.
Answer: gradient 6; y-intercept 0
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.Find the gradient of the line through (−4, −1) and (−9, 8).
Answer: −
- gradient = rise ÷ run = (8 − (−1)) ÷ (−9 − (−4))
- = 9 ÷ −5 = −
7.For the line y = 6x − 4, write the gradient and the y-intercept.
Answer: gradient 6; 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.
8.A line has a gradient of 2 and passes through (−1, −7). Find its equation.
Answer: y = 2x − 5
- y = 2x + (y-intercept)
- −7 = 2 × (−1) + (y-intercept)
- y-intercept = −7 − (−2) = −5
- y = 2x − 5
9.Find the gradient of the line through (−5, 0) and (−10, −6).
Answer:
- gradient = rise ÷ run = (−6 − 0) ÷ (−10 − (−5))
- = −6 ÷ −5 =
10.A line has a gradient of −4 and passes through (−4, 10). Find its equation.
Answer: y = −4x − 6
- y = −4x + (y-intercept)
- 10 = −4 × (−4) + (y-intercept)
- y-intercept = 10 − 16 = −6
- y = −4x − 6
Marking tips
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