Question

for the function $f(x)=x^{2}-4x + 8$, find the slope of the secant line between $x=-1$ and $x = 7$.

Explanation:

Step1: Find function values at given points

First, find $f(-1)$ and $f(7)$.
For $x=-1$:
$f(-1)=(-1)^2 - 4\times(-1)+8=1 + 4+8=13$.
For $x = 7$:
$f(7)=7^2-4\times7 + 8=49-28 + 8=29$.

Step2: Use 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, $x_1=-1,y_1 = f(-1)=13,x_2=7,y_2=f(7)=29$.
$m=\frac{f(7)-f(-1)}{7-(-1)}=\frac{29 - 13}{7 + 1}=\frac{16}{8}=2$.

Answer:

$2$