for the function $f(x)=2x^{2}-5x - 8$, find the slope of the secant line between $x = 3$ and $x = 5$.

Question

Accepted Answer

# Explanation:
## Step1: Find $f(3)$
Substitute $x = 3$ into $f(x)=2x^{2}-5x - 8$.
$$
\begin{align*}
f(3)&=2\times3^{2}-5\times3 - 8\
&=2\times9-15 - 8\
&=18-15 - 8\
&=-5
\end{align*}
$$
## Step2: Find $f(5)$
Substitute $x = 5$ into $f(x)=2x^{2}-5x - 8$.
$$
\begin{align*}
f(5)&=2\times5^{2}-5\times5 - 8\
&=2\times25-25 - 8\
&=50-25 - 8\
&=17
\end{align*}
$$
## Step3: Calculate the slope of the secant line
The slope $m$ of 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 $x_1 = 3,y_1=f(3)=-5,x_2 = 5,y_2=f(5)=17$.
$$
\begin{align*}
m&=\frac{f(5)-f(3)}{5 - 3}\
&=\frac{17-(-5)}{2}\
&=\frac{17 + 5}{2}\
&=\frac{22}{2}\
&=11
\end{align*}
$$
# Answer:
11

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find \(f(3)\)

Step2: Find \(f(5)\)

Step3: Calculate the slope of the secant line

Answer: