Answer
$y=\dfrac{\sqrt 3}{3}(x-4)$
Work Step by Step
$r \cos (\theta+\dfrac{\pi}{3})=4 \sqrt 3$
or, $r[\cos \theta \cos \dfrac{\pi}{3}-\sin \theta \sin \dfrac{\pi}{3}]=4\sqrt 3$
or, $r \cos \theta -\sqrt 3 r \sin \theta=4\sqrt 3$
This can be re-arranged as: $x-(\sqrt 3) y =4\sqrt 3$
Thus, $y=\dfrac{\sqrt 3}{3}(x-4)$
