Two linear forms of the same law

The variables \(x\) and \(y\) are related by \(y=\dfrac{a}{x+b}\), where \(a\) and \(b\) are positive constants.

1. Show that the graph of \(\dfrac{1}{y}\) against \(x\) is a straight line, and state its gradient and intercept in terms of \(a\) and \(b\).[2]
2. This line has gradient \(0.25\) and vertical intercept \(0.5\). Find \(a\) and \(b\).[2]
3. Another student plots \(x\) against \(\dfrac{1}{y}\) for the same data. Find the gradient and intercept of her line, and explain why both students obtain the same values of \(a\) and \(b\).[2]
4. Explain why plotting \(y\) against \(\dfrac{1}{x}\) does not give a straight line.[2]