How do I get the equation of the line given this slope and graph?

How do I get the equation of the line given this slope and graph?

This might be really low level for you guys but I just don't understand.!
The graph is $y=1/(x-1)$ and the given slope is $-1$.
I have to get the equation of the tangent line given the slope and graph.
So, I tried making it equal $y=-x+k$
I got $$x^2-x-kx-k+1=0$$ I tried performing the quadratic on it and got it
down to: $$k^2+6k-3=0$$ I'm just really confused now and the book doesn't
explain what to do...
Thanks for any input...