Question

question
for the function f(x) = x^2 - 4, find the slope of the secant line between x = 2 and x = 5.

Explanation:

Step1: Find function values at given points

First, find $f(2)$ and $f(5)$.
For $x = 2$, $f(2)=2^{2}-4=4 - 4=0$.
For $x = 5$, $f(5)=5^{2}-4=25 - 4 = 21$.

Step2: Use slope formula for secant line

The slope $m$ of the secant line between two points $(x_1,y_1)$ and $(x_2,y_2)$ on the graph of $y = f(x)$ is $m=\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here $x_1 = 2$, $x_2=5$, $f(x_1)=0$, $f(x_2)=21$. So $m=\frac{21 - 0}{5 - 2}=\frac{21}{3}=7$.

Answer:

7