4400 Higher November 2005 Paper 4 Q12
12 The charge, £\(y\), for hiring a bike for \(x\) hours can be found from the straight line \(\mathbf{L}\).
(a)
(i) Find the gradient of the line \(\mathbf{L}\).
(ii) Give an interpretation of your gradient. (3)
(b) Write down the equation of the line \(\mathbf{L}\). (2)
(c) Another bike hire shop charges £3 with an additional charge of £1.50 per hour.
Find the time for which the two shops’ charges are equal. (2)
Find the time for which the two shops’ charges are equal. (2)
| Scheme | Marks |
|---|---|
| (i) vertical ÷ horizontal | M1 |
| 2 | A1 |
| (ii) hourly charge oe | B1 |
| (3) |
| Scheme | Marks |
|---|---|
| \(y = 2x + 1\) | B1 B1 |
| (2) |
Notes
B1f: (his 2)\(x\) ; B1: +1 ; −B1 if no ‘\(y =\)’
| Scheme | Marks |
|---|---|
| line through (0, 3) grad = 1.5 or \(1 + 2x = 3 + 1.5x\) | M1 |
| 4 | A1 |
| (2) | |
| (7 marks) |