Least value predicted by a linearised law

For \(x>0\), the variables \(x\) and \(y\) satisfy \(y=ax+\dfrac{b}{x}\), where \(a\) and \(b\) are constants. The graph of \(xy\) against \(x^2\) is a straight line through \((1,5)\) and \((9,13)\).

1. Explain why plotting \(xy\) against \(x^2\) gives a straight line, and find \(a\) and \(b\).[3]
2. By writing \(y\) in the form \(\left(\sqrt{x}-\dfrac{p}{\sqrt{x}}\right)^2+q\), show that \(y\ge4\) for all \(x>0\), and find the value of \(x\) at which \(y=4\).[3]
3. A recorded reading is \(y=3.5\) at \(x=1.5\). Explain what this suggests about the reading.[1]