4MA0 Higher January 2017 Paper 4 Q12
12 The straight line L has equation \(\;3x - 2y = 15\)
(a) Find the gradient of L. (3)
(b) Find the coordinates of the point where L crosses the \(y\)-axis. (1)
(c) Find an equation of the line that is parallel to L and crosses the \(x\)-axis at (−2, 0) (2)
| Scheme | Marks |
|---|---|
| \(2y = 3x - 15\) or \(-2y = 15 - 3x\) or \(1.5x - y = 7.5\) | M1 |
| \(y = 1.5x - 7.5\) or \(y = \dfrac{3x - 15}{2}\) or \(y = \dfrac{15 - 3x}{-2}\) oe | M1 |
| 1.5 | A1 |
| (3) |
Notes
M1: Or for finding the coordinates of two correct points that lie on the line
M1: or \(\dfrac{\text{difference of } y \text{ values}}{\text{difference of } x \text{ values}}\) for any two correct points on the line
A1: oe
Do not penalise a mistake in the constant term if the correct answer is given.
SCB2 for \(1.5x\)
SCB1 ft from their \(y = ax + b\)
| Scheme | Marks |
|---|---|
| (0, −7.5) | B1 |
| (1) |
Notes
B1: oe
| Scheme | Marks |
|---|---|
| \(0 = 1.5 \times -2 + c\) or \(3 \times -2 = k\) or \(y - 0 = 1.5(x - -2)\) | M1 |
| \(y = 1.5x + 3\) | A1 |
| (2) | |
| (6 marks) |
Notes
M1: ft 1.5 from (a) or \(c = 3\)
A1: ft 1.5 from (a)
or \(3x - 2y = -6\) or \(y = 1.5(x + 2)\)
oe