This is for my advanced functions course so NO CALCULUS is used. Please help find the equation.

Find the equation of the line with slope -1 that is the tangent to the curve y=1/(x-1).

This is my work until I get stuck.

y=-1x+k

-1x+k=1/(x-1)

y=??

I get stuck from here. Can someone please solve this completely and be exact with the steps. Thanks!