4MA0 Higher June 2016 Paper 3 Q13
13 The straight line L passes through the points (−2, 3) and (6, 9)
Find an equation of the line that is parallel to L and passes through the point (5, −1)
Give your answer in the form \(ax + by = c\) where \(a\), \(b\) and \(c\) are integers.
(5)
| Scheme | Marks |
|---|---|
| e.g. \(\dfrac{9 - 3}{6 - -2} \left(= \dfrac{3}{4}\right)\) | M1 |
| \(y = \text{"}0.75\text{"}x + c\) | M1 |
| \(-1 = \text{"}0.75\text{"} \times 5 + c\) \(\left(c = -\dfrac{19}{4}\right)\) | M1 |
| \(y = \dfrac{3}{4}x + -\dfrac{19}{4}\) oe | A1 |
| \(4y - 3x = -19\) | A1 |
| (5) |
Notes
M1: for method to find gradient of L
M1: use of their gradient in an equation
\(c\) may be numerical
M1: method to find \(c\)
A1: correct equation
(equation in any form)
A1: oe with integer coefficients
e.g. \(3x - 4y = 19\); \(4y = 3x - 19\)
M2 for \(y - -1 = \text{"}\dfrac{3}{4}\text{"}(x - 5)\) oe