Answer
$y=\dfrac{\sqrt 3}{3}x-4$
Work Step by Step
Here, we have $r \cos (\theta+\dfrac{\pi}{3})=4 \sqrt 3$
This implies that
$r[\cos \theta \cos \dfrac{\pi}{3}-\sin \theta \sin \dfrac{\pi}{3}]=4\sqrt 3$
or, $r \cos \theta -\sqrt 3 r \sin \theta=4\sqrt 3$
Thus, we have $x-\sqrt 3 y =4\sqrt 3\implies y=\dfrac{\sqrt 3}{3}x-4$
