question
for the function ( f(x)=x^{2}+4x + 9 ), find the slope of the secant
line between ( x=-6 ) and ( x=-3 ).

Question

Accepted Answer

# Explanation:
## Step1: Find $ f(-6) $
Substitute $ x = -6 $ into $ f(x)=x^{2}+4x + 9 $:
$$
\begin{align*}
f(-6)&=(-6)^{2}+4\times(-6)+9\
&=36-24 + 9\
&=21
\end{align*}
$$
## Step2: Find $ f(-3) $
Substitute $ x=-3 $ into $ f(x)=x^{2}+4x + 9 $:
$$
\begin{align*}
f(-3)&=(-3)^{2}+4\times(-3)+9\
&=9-12 + 9\
&=6
\end{align*}
$$
## Step3: Calculate the slope of the secant line
The slope formula for the secant line between two points $(x_1,f(x_1))$ and $(x_2,f(x_2))$ is $m=\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here $x_1=-6,f(x_1) = 21,x_2=-3,f(x_2)=6$
$$
\begin{align*}
m&=\frac{6 - 21}{-3-(-6)}\
&=\frac{-15}{3}\
&=- 5
\end{align*}
$$

# Answer:
$-5$

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QUESTION IMAGE

Question

Explanation:

Step1: Find \( f(-6) \)

Step2: Find \( f(-3) \)

Step3: Calculate the slope of the secant line

Answer: