Using transformed coordinates to make predictions

Variables \(x>0\) and \(y\) satisfy \(y=px+q/x\). A graph of \(xy\) against \(x^2\) passes through \((1,10)\) and \((9,26)\).

1. Find \(p\) and \(q\).[3]
2. Find \(y\) when \(x=3.5\), correct to 3 significant figures.[2]
3. Find the positive value of \(x\) for which \(y=3x\).[2]