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

Question

Accepted Answer

# Explanation:
## Step1: Find $ f(-6) $
Substitute $ x = -6 $ into $ f(x)=-x^{2}-3x + 6 $:
$$
\begin{align*}
f(-6)&=-(-6)^{2}-3\times(-6)+6\
&=-36 + 18+6\
&=-12
\end{align*}
$$
## Step2: Find $ f(4) $
Substitute $ x = 4 $ into $ f(x)=-x^{2}-3x + 6 $:
$$
\begin{align*}
f(4)&=-4^{2}-3\times4+6\
&=-16-12 + 6\
&=-22
\end{align*}
$$
## Step3: Calculate the slope of the secant line
The slope formula for the secant line between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here $x_1=-6,y_1 = f(-6)=-12,x_2 = 4,y_2=f(4)=-22$
$$
\begin{align*}
m&=\frac{-22-(-12)}{4-(-6)}\
&=\frac{-22 + 12}{4 + 6}\
&=\frac{-10}{10}\
&=-1
\end{align*}
$$
# Answer:
$-1$

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QUESTION IMAGE

Question

Explanation:

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

Step2: Find \( f(4) \)

Step3: Calculate the slope of the secant line

Answer: