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