Answer
$x+y=2$
.
Work Step by Step
Apply identity for $\cos(\alpha-\beta)$
$\displaystyle \cos(\theta-\frac{\pi}{4})=\cos\theta\cos\frac{\pi}{4}+\sin\theta\sin\frac{\pi}{4}$
$\displaystyle \cos(\theta-\frac{\pi}{4})=\frac{1}{\sqrt{2}}\cdot\cos\theta+\frac{1}{\sqrt{2}}\cdot\sin\theta\qquad/\times r$
$r\displaystyle \cos(\theta-\frac{\pi}{4})=\frac{1}{\sqrt{2}}\cdot(r\cos\theta)+\frac{1}{\sqrt{2}}\cdot(r\sin\theta)$
Apply the conversion formula$\quad (x,y)=(r\cos\theta,r\sin\theta)$
$r\displaystyle \cos(\theta-\frac{\pi}{4})=\frac{1}{\sqrt{2}}\cdot x+\frac{1}{\sqrt{2}}\cdot y$
In Cartesian coordinates, the line equation is
$\displaystyle \frac{1}{\sqrt{2}}\cdot x+\frac{1}{\sqrt{2}}\cdot y=\sqrt{2}\qquad/\times\sqrt{2}$
$x+y=2$
