Answer
$ y=x+1$
Work Step by Step
Consider $r \cos (\theta-\dfrac{3\pi}{4})=\dfrac{ \sqrt 2}{2}$
or, $r[\cos \theta \cos \dfrac{3\pi}{4}+\sin \theta \sin \dfrac{3\pi}{4}]=\dfrac{ \sqrt 2}{2}$
This can be re-arranged as: $-x+y=1 \implies y=x+1$
