Question

given $f(x)=x^2 + x$, find the equation of the secant line passing through $(-6, f(-6))$ and $(2, f(2))$. write your answer in the form $y = mx + b$.

Explanation:

Step1: Calculate f(-6)

$f(-6)=(-6)^2 + (-6)=36 - 6=30$

Step2: Calculate f(2)

$f(2)=(2)^2 + 2=4 + 2=6$

Step3: Find slope m

$m=\frac{f(2)-f(-6)}{2-(-6)}=\frac{6-30}{8}=\frac{-24}{8}=-3$

Step4: Solve for b using (2,6)

$6=-3(2)+b \implies 6=-6 + b \implies b=12$

Answer:

$y=-3x + 12$