Answer
$\displaystyle \frac{dx}{dy}=\frac{1}{8}$
Work Step by Step
$\displaystyle \frac{dx}{dy}=\frac{1}{(\frac{dy}{dx})},\qquad \frac{dy}{dx}\neq 0$
$\displaystyle \frac{dy}{dx}=\frac{d}{dx}[8x+4]=8$
$\displaystyle \frac{dx}{dy}=\frac{1}{8}$