Answer the whole of this question on a piece of graph paper.
The taxi fare, \(\$y\), charged by Taxi Company A, for a journey is given by \(y=4+0.55x\), where \(x\) is the distance travelled in km. Some corresponding values of \(x\) and \(y\) are given in the following table:
| Distance, \(x\) (km) | 2 | 12 | 20 |
| Taxi fare, \(\$y\) | 5.1 | \(p\) | 15 |
Find the value of \(p\).[1]
Using a scale of \(1\) cm to represent \(2\) units on the \(x\)-axis and \(1\) cm to represent \(1\) unit on the \(y\)-axis, draw the graph of \(y=4+0.55x\) for \(0\le x\le24\).[3]
Explain the significance of the number \(4\) in the given context.[1]
The charges of Taxi Company B can be modelled by the equation \(y=6+0.3x\).
Explain what the number \(0.3\) means in the given context.[1]
By adding another line on the same axes drawn in (a), find the solution to the simultaneous equations \(y=4+0.55x\) and \(y=6+0.3x\).[3]
Use your graphs to advise your friend who wants to hire a taxi from one of these two companies.[1]