Comparing two affine taxi fares

Core stretch

Use continuous linear fare models; ignore rounding to charging intervals and any additional fees.

Taxi company ABC charges a \(\$4.00\) flag-down fare plus \(\$0.30\) per \(0.5\) km.

1. Find the fare for \(9.5\) km.[2]
2. Find the distance for a \(\$16\) fare.[2]
3. Write a formula connecting fare \(y\) and distance \(d\).[2]
4. Company PQR uses the supplied graph. Explain whether its \(y\) is directly proportional to \(d\).[2]
5. Which company is cheaper for \(3\) km? Justify.[2]
6. What is the maximum distance for which that chosen company is no more expensive?[2]