Use the limit process to find the slope of the graph of the following function at the point $( 5 , - 27 )$.
$$g ( x ) = - 7 - 4 x$$
A) $- 11$
B) $- 27$
C) $- 3$
D) $- 4$
E) 5

Question

Quizplus · Accepted Answer

We use the limit definition of slope:
\begin{align*}
m &= \lim_{h 	o 0} \frac{f(5+h)-f(5)}{h} \
&= \lim_{h 	o 0} \frac{-7-4(5+h)-(-7-4(5))}{h} \
&= \lim_{h 	o 0} \frac{-4h}{h} \
&= -4
\end{align*}
Therefore, the slope of the graph of $g(x)$ at $(5,-27)$ is $-4$.

Use the Limit Process to Find the Slope of the Graph