Answer
$r=\dfrac{8}{2 \cos \theta+3 \sin \theta}$
Work Step by Step
Given: $2x+3y=8$
We need to use the formulas: $x =r \cos \theta; y= r \sin \theta$ to get the polar equation.
$2x+3y=8 \implies 2r \cos \theta+3r \sin \theta=8$
$r( 2 \cos \theta+3 \sin \theta)=8$
This gives:
$r=\dfrac{8}{2 \cos \theta+3 \sin \theta}$
