Question

find the slope of the secant line between $x = 2$ and $x = 5$ on the graph of the function $f(x)=x^{2}-2x + 5$. provide your answer below: $m_{sec}=square$

Explanation:

Step1: Find $f(2)$

$f(2)=2^{2}-2\times2 + 5=4 - 4+5=5$

Step2: Find $f(5)$

$f(5)=5^{2}-2\times5 + 5=25-10 + 5=20$

Step3: Use slope formula

The slope $m_{sec}$ of the secant line between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m_{sec}=\frac{y_2 - y_1}{x_2 - x_1}$. Here $x_1 = 2,y_1=f(2)=5,x_2 = 5,y_2=f(5)=20$. So $m_{sec}=\frac{20 - 5}{5 - 2}=\frac{15}{3}=5$

Answer:

$5$