## Precalculus (6th Edition) Blitzer

$r=\dfrac{8}{2 \cos \theta+3 \sin \theta}$
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: $r=\dfrac{8}{2 \cos \theta+3 \sin \theta}$