How do I prove that a line is perpendicular to a plane given their conditions? How can I extract a vector out of the line condition?

Question

Given the condition of a line $l:-x=z-1 \land y=1$, and the condition of a plane $\alpha:x-z=0$, how can I prove that $l\perp\alpha$?

I know that the vector normal to $\alpha$, will be parallel to the line, and that this vector is $\vec{n}(1,0,-1)$, but how do I extract a vector from the line condition to do the dot product with $\vec{n}$?