Answer
The required equation in the polar form is $r=\frac{7}{5\,\cos \,\theta -\sin \,\theta }$.
Work Step by Step
We know that $x=r\,\cos \,\theta \ \text{ and }\ y=r\,\sin \,\theta $.
Substitute $x=r\,\cos \,\theta \ \text{ and }\ y=r\,\sin \,\theta $ in the given equation $5x-y=7.$
Therefore,
$\begin{align}
& 5x-y=7 \\
& 5\left( r\,\cos \,\theta \right)-r\,\sin \,\theta =7 \\
& r\left( 5\,\cos \,\theta -\sin \,\theta \right)=7
\end{align}$
and
$r=\frac{7}{5\,\cos \,\theta -\sin \,\theta }$
