Question

if $f(x)=4x + 12$, find the slope of the secant line between the values of $x_1=-9$ and $x_2 = 8$.

Explanation:

Step1: Find $f(x_1)$

Substitute $x_1=-9$ into $f(x)=4x + 12$.
$f(x_1)=4\times(-9)+12=-36 + 12=-24$

Step2: Find $f(x_2)$

Substitute $x_2 = 8$ into $f(x)=4x + 12$.
$f(x_2)=4\times8+12=32 + 12=44$

Step3: Calculate the slope of the secant line

The slope formula of the secant line between two points $(x_1,f(x_1))$ and $(x_2,f(x_2))$ is $m=\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.
$m=\frac{44-(-24)}{8-(-9)}=\frac{44 + 24}{8 + 9}=\frac{68}{17}=4$

Answer:

$4$