Answer: \(y=\left(\dfrac{10}{x}+4\right)^4\).

Let

\(Y=\sqrt[4]{y} \qquad\text{and}\qquad X=\frac1x.\)

The graph of \(Y\) against \(X\) is a straight line through \((0.5,9)\) and \((3,34)\). Its gradient is

\(m=\frac{34-9}{3-0.5}=\frac{25}{2.5}=10.\)

So the line has equation

\(Y=10X+c.\)

Using \((0.5,9)\),

\(9=10(0.5)+c.\)

Thus

\(c=4.\)

Therefore

\(\sqrt[4]{y}=10\left(\frac1x\right)+4.\)

Hence

\(y=\left(\frac{10}{x}+4\right)^4.\)