## Precalculus (6th Edition) Blitzer

The required equation in the polar form is $r=\frac{7}{5\,\cos \,\theta -\sin \,\theta }$.
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 $r=\frac{7}{5\,\cos \,\theta -\sin \,\theta }$