Problem

A curve passes through the point $\big(\frac{4}{5}, -3\big)$ and is such that $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{-20}{(5x - 3)^2}$.

(a) Find the equation of the curve.

(b) The curve is transformed by a stretch in the $x$-direction with scale factor $\frac{1}{2}$ followed by a translation of $\begin{pmatrix}2 \\ 10\end{pmatrix}$.

Find the equation of the new curve.