Answer
$\displaystyle \frac{dx}{dy}=\frac{1}{3}$
Work Step by Step
$\displaystyle \frac{dx}{dy}=\frac{1}{(\frac{dy}{dx})},\qquad \frac{dy}{dx}\neq 0$
$\displaystyle \frac{dy}{dx}=\frac{d}{dx}[3x-2]=3$
$\displaystyle \frac{dx}{dy}=\frac{1}{3}$