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