4MA0 Higher June 2017 Paper 4 Q13
13 Here are the equations of four straight lines.
| Line A | \(y = 2x + 3\) |
| Line B | \(2y = 6 - 3x\) |
| Line C | \(4x - 2y = 3\) |
| Line D | \(y = 3 - 2x\) |
Two of these lines are parallel.
(a) Which two lines? (2)
Line L has a gradient of \(-\dfrac{5}{2}\) and passes through the point with coordinates (1, 3)
(b) Find an equation of L.
Give your answer in the form \(ax + by = c\) where \(a\), \(b\) and \(c\) are integers. (3)
Give your answer in the form \(ax + by = c\) where \(a\), \(b\) and \(c\) are integers. (3)
| Scheme | Marks |
|---|---|
| \(y = 3 - 1.5x\) or \(2x - 1.5 = y\) or \(m = 2\) (A) or \(m = -1.5\) (B) or \(m = 2\) (C) or \(m = -2\) (D) | M1 |
| A and C | A1 |
| (2) |
Notes
M1: If using gradients, must state \(m\) = or gradient =
A1: (allow correct equations listed)
| Scheme | Marks |
|---|---|
| \(y = -\dfrac{5}{2}x + c\) or \(y - y_1 = -\dfrac{5}{2}(x - x_1)\) | M1 |
\(3 = -\dfrac{5}{2} \times 1 + c\) or \(c = \dfrac{11}{2}\) oe or \(y = -\dfrac{5}{2}x + \dfrac{11}{2}\) or \(y - 3 = -\dfrac{5}{2}(x - 1)\) or \(2(y - 3) = -5(x - 1)\) | M1 |
| \(5x + 2y = 11\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: \(c\) can be any value,
e.g. \(y = -\dfrac{5}{2}x + 3\)
A1: oe eg. \(10x + 4y = 22\) or in a different but correct form but must have integer values,
e.g. \(2y = -5x + 11\)