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