4MA0 Higher June 2013 Paper 3R Q13
13 The points with coordinates (0, 3) and (8, 5) lie on the straight line L.
(a) Work out the gradient of L. (2)
(b) Write down an equation of L. (1)
(c) Find an equation of the line which is parallel to L and which passes through the point (−4, −2) (2)
| Scheme | Marks |
|---|---|
| Correct v ÷ h eg 2 ÷ 8 or \(\dfrac{5 - 3}{8 - 0}\) oe | M1 |
| 0.25 oe | A1 |
| (2) |
Notes
M1: or \(y = mx + 3\) with any \((x, y)\) on L substituted eg. \(5 = 8m + 3\)
| Scheme | Marks |
|---|---|
| \(y = \text{“}0.25\text{”}x + 3\) oe | B1 ft |
| (1) |
Notes
B1 ft: Accept equivalents (e.g. \(4y = x + 12\))
Gradient used must be 0.25 or the gradient found in (a)
| Scheme | Marks |
|---|---|
| M1ft | |
| \(y = \text{“}0.25\text{”}x - 1\) oe e.g. \(4y = x - 4\) | A1ft |
| (2) |
Notes
M1ft: for \(y = \text{“}0.25\text{”}x + c\) (\(c \neq -1\))
or \(c = -1\) as a statement
or \(\text{“}0.25\text{”}x - 1\)
or \(L = \text{“}0.25\text{”}x - 1\)
or \(-2 = \text{“}0.25\text{”} \times -4 + c\) (corrected from the printed mark scheme: printed as “× 4”)
A1ft: from “0.25” with \(c = -1\) or \(c\) evaluated
Gradient used must be 0.25 or the gradient found in (a)