Answer
slope$=-4$
See graph.
Work Step by Step
1. Find the derivative of $f(x)=x^2-2x+3$ as $f'(x)=2x-2$.
2. The slope of the tangent line is the same as the derivative at $x=-1$, we have $m=2(-1)-2=-4$
3. The tangent line is $y-6=-4(x+1)$ or $y=-4x+2$
4. See graph.