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Year 10 Mathematics · Gradient and linear graphs

Name: ______________________

Date: ____________

1. What is the gradient of the line y = 5x − 7?
- ☐ (a) −7
- ☐ (b) 5
- ☐ (c) 7
- ☐ (d) −5
2. What is the y-intercept of the line y = 2x + 9?
- ☐ (a) 2
- ☐ (b) −9
- ☐ (c) 11
- ☐ (d) 9
3. Find the gradient of the line through (2, 1) and (6, 9).
- ☐ (a) 2
- ☐ (b) 1/2
- ☐ (c) 4
- ☐ (d) 8
4. A line slopes downwards from left to right. Which statement is true?
- ☐ (a) It has a positive gradient
- ☐ (b) It has a gradient of zero
- ☐ (c) It has a negative gradient
- ☐ (d) It has no y-intercept
5. Which point lies on the line y = 3x + 1?
- ☐ (a) (1, 3)
- ☐ (b) (0, 3)
- ☐ (c) (3, 9)
- ☐ (d) (2, 7)
6. Find the gradient of the line through (−1, 4) and (3, −4).
7. For the line y = 4x − 3, find the value of y when x = 5.
8. What is the gradient of the horizontal line y = 6?

Answer sheet

1. 5 — In y = mx + c the gradient is m, the coefficient of x, which is 5.
2. 9 — In y = mx + c the y-intercept is c, which is 9. Check: when x = 0, y = 9.
3. 2 — Rise = 9 − 1 = 8 and run = 6 − 2 = 4, so the gradient is 8 ÷ 4 = 2.
4. It has a negative gradient — Lines that fall from left to right have a negative gradient.
5. (2, 7) — Substitute x = 2: y = 3 × 2 + 1 = 7, so (2, 7) is on the line. The other points do not satisfy the equation.
6. −2 — Rise = −4 − 4 = −8 and run = 3 − (−1) = 4, so the gradient is −8 ÷ 4 = −2.
7. 17 — y = 4 × 5 − 3 = 20 − 3 = 17.
8. 0 — A horizontal line has no rise, so its gradient is 0 ÷ run = 0.