## Precalculus (6th Edition) Blitzer

$r=\frac{7}{3\cos \theta +\sin \theta }$.
The rectangular equation is: $3x+y=7$ …… (1) The relation between polar coordinates and rectangular coordinates is expressed as below: $x=r\cos \theta$ and $y=r\sin \theta$ …… (2) Substituting the values of $x\ \text{ and }\ y$ from (2) in (1), we get \begin{align} & 3x+y=7 \\ & 3r\cos \theta +r\sin \theta =7 \\ & r\left( 3\cos \theta +\sin \theta \right)=7 \\ & r=\frac{7}{\left( 3\cos \theta +\sin \theta \right)} \end{align} Hence the obtained polar expression is $r=\frac{7}{3\cos \theta +\sin \theta }$.