Year 9 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 4 — 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 3 — 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.A line has a gradient of 1 and passes through (4, 0). Find its equation.
Answer: y = x − 4
- y = 1x + (y-intercept)
- 0 = 1 × 4 + (y-intercept)
- y-intercept = 0 − 4 = −4
- y = x − 4
2.A line has a gradient of −1 and passes through (1, −6). Find its equation.
Answer: y = −x − 5
- y = −1x + (y-intercept)
- −6 = −1 × 1 + (y-intercept)
- y-intercept = −6 − (−1) = −5
- y = −x − 5
3.A line has a gradient of −2 and passes through (−4, 16). Find its equation.
Answer: y = −2x + 8
- y = −2x + (y-intercept)
- 16 = −2 × (−4) + (y-intercept)
- y-intercept = 16 − 8 = 8
- y = −2x + 8
4.A line has a gradient of 2 and passes through (3, 5). Find its equation.
Answer: y = 2x − 1
- y = 2x + (y-intercept)
- 5 = 2 × 3 + (y-intercept)
- y-intercept = 5 − 6 = −1
- y = 2x − 1
5.A line has a gradient of 3 and passes through (2, 4). Find its equation.
Answer: y = 3x − 2
- y = 3x + (y-intercept)
- 4 = 3 × 2 + (y-intercept)
- y-intercept = 4 − 6 = −2
- y = 3x − 2
6.For the line y = 6x + 2, write the gradient and the y-intercept.
Answer: gradient 6; y-intercept 2
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.A line has a gradient of 5 and passes through (−4, −14). Find its equation.
Answer: y = 5x + 6
- y = 5x + (y-intercept)
- −14 = 5 × (−4) + (y-intercept)
- y-intercept = −14 − (−20) = 6
- y = 5x + 6
8.A line has a gradient of 4 and passes through (1, −1). Find its equation.
Answer: y = 4x − 5
- y = 4x + (y-intercept)
- −1 = 4 × 1 + (y-intercept)
- y-intercept = −1 − 4 = −5
- y = 4x − 5
9.For the line y = −3x − 1, write the gradient and the y-intercept.
Answer: gradient −3; y-intercept −1
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.Does the point (4, −12) lie on the line y = −2x − 4?
- AYes
- BNo
Answer: Yes
Substitute x = 4: y = −2 × 4 − 4 = −12, which matches.
Marking tips
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