Question

given $h(x)=x^3 + 2$, find the equation of the secant line passing through $(-3, h(-3))$ and $(1, h(1))$. write your answer in the form $y = mx + b$.

Explanation:

Step1: Calculate h(-3)

$h(-3)=(-3)^3 + 2=-27 + 2=-25$

Step2: Calculate h(1)

$h(1)=(1)^3 + 2=1 + 2=3$

Step3: Find slope m

$m=\frac{h(1)-h(-3)}{1-(-3)}=\frac{3-(-25)}{4}=\frac{28}{4}=7$

Step4: Solve for b using (1,3)

$3=7(1)+b \Rightarrow b=3-7=-4$

Answer:

$y=7x-4$