Question

question
find the slope of the secant line between (x = - 3) and (x = 3) on the graph of the function (f(x)=3x^{2}-x + 1).

provide your answer below:

Explanation:

Step1: Find function values

First, find $f(-3)$ and $f(3)$.
For $x=-3$, $f(-3)=3(-3)^2-(-3)+1=3\times9 + 3+1=27 + 3+1=31$.
For $x = 3$, $f(3)=3\times3^2-3 + 1=3\times9-3 + 1=27-3 + 1=25$.

Step2: Apply slope formula

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, $x_1=-3,y_1 = 31,x_2=3,y_2 = 25$.
So $m=\frac{25 - 31}{3-(-3)}=\frac{-6}{6}=-8$.

Answer:

-8