Year 9 Gradient and Linear Equations Worksheet — Level 2 — 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 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.A line has a gradient of 3 and passes through (−3, −14). Find its equation.
Answer: y = 3x − 5
- y = 3x + (y-intercept)
- −14 = 3 × (−3) + (y-intercept)
- y-intercept = −14 − (−9) = −5
- y = 3x − 5
2.A line has a gradient of −3 and passes through (1, 1). Find its equation.
Answer: y = −3x + 4
- y = −3x + (y-intercept)
- 1 = −3 × 1 + (y-intercept)
- y-intercept = 1 − (−3) = 4
- y = −3x + 4
3.A line has a gradient of −5 and passes through (−1, 9). Find its equation.
Answer: y = −5x + 4
- y = −5x + (y-intercept)
- 9 = −5 × (−1) + (y-intercept)
- y-intercept = 9 − 5 = 4
- y = −5x + 4
4.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
5.A line has a gradient of 3 and passes through (2, 6). Find its equation.
Answer: y = 3x
- y = 3x + (y-intercept)
- 6 = 3 × 2 + (y-intercept)
- y-intercept = 6 − 6 = 0
- y = 3x
6.Find the gradient of the line through (−1, −1) and (3, 3).
Answer: 1
- gradient = rise ÷ run = (3 − (−1)) ÷ (3 − (−1))
- = 4 ÷ 4 = 1
7.For the line y = 6x − 3, write the gradient and the y-intercept.
Answer: gradient 6; y-intercept −3
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.For the line y = −5x + 5, write the gradient and the y-intercept.
Answer: gradient −5; y-intercept 5
In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.
9.Find the gradient of the line through (1, −1) and (−2, −4).
Answer: 1
- gradient = rise ÷ run = (−4 − (−1)) ÷ (−2 − 1)
- = −3 ÷ −3 = 1
10.Find the gradient of the line through (−1, 0) and (−2, 2).
Answer: −2
- gradient = rise ÷ run = (2 − 0) ÷ (−2 − (−1))
- = 2 ÷ −1 = −2
Marking tips
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