Answer
$-4$
Work Step by Step
Consider that the tangent line contains the point $(x, c)$. The slope of the tangent line to the graph of $f(x)$ at $(x, c)$ can be written as
$f'(x) =\lim\limits_{x \to c} \dfrac{f(x)-f(c)}{x-c}$
Consider $c=3$ and $f(x)=-4x+5$. Thus, we have:
$f'(x) =\lim\limits_{x \to 3} \dfrac{f(x)-f(3)}{x-3} \\=\lim\limits_{x \to 3} \dfrac{-4x+5-(-7)}{x-3} \\=\lim\limits_{x \to 3} \dfrac{-4(x-3)}{x-3}\\=-4 $