Question

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_{\text{sec}}=square)

Explanation:

Step1: Find $f(2)$

Substitute $x = 2$ into $f(x)$:
$f(2)=2^{2}-2\times2 + 5=4 - 4+5 = 5$

Step2: Find $f(5)$

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

Step3: Use slope formula

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

Answer:

$5$