Answer
$r=\frac{7}{3\cos \theta +\sin \theta }$.
Work Step by Step
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 $r=\frac{7}{3\cos \theta +\sin \theta }$.
