Answer
$m=-2$
Work Step by Step
$f(x)=5-2x,$ at $(-3,11)$
The slope of the tangent line at the point $P(a,f(a))$ is given by $m=\lim_{h\to0}\dfrac{f(a+h)-f(a)}{h}$
In this case, $a=-3$
Find $f(a+h)$ by substituting $x$ by $-3+h$ in $f(x)$ and simplifying:
$f(-3+h)=5-2(-3+h)=5+6-2h=11-2h$
Find $f(a)$ by substituting $x$ by $-3$ in $f(x)$ and simplifying:
$f(-3)=5-2(-3)=5+6=11$
Substitute the known values into the formula that gives the slope of the tangent line and evaluate:
$m=\lim_{h\to0}\dfrac{f(-3+h)-f(-3)}{h}=\lim_{h\to0}\dfrac{(11-2h)-11}{h}=...$
$...=\lim_{h\to0}\dfrac{-2h}{h}=\lim_{h\to0}-2=-2$
