Question

given $g(x)=x^2 - 5x$, find the equation of the secant line passing through $(-3, g(-3))$ and $(4, g(4))$. write your answer in the form $y = mx + b$.

Explanation:

Step1: Calculate g(-3)

$g(-3)=(-3)^2 -5(-3)=9 +15=24$

Step2: Calculate g(4)

$g(4)=4^2 -5(4)=16 -20=-4$

Step3: Find slope m

$m=\frac{g(4)-g(-3)}{4-(-3)}=\frac{-4-24}{7}=\frac{-28}{7}=-4$

Step4: Solve for intercept b

Use point (-3,24): $24=-4(-3)+b\Rightarrow24=12+b\Rightarrow b=12$

Answer:

$y=-4x+12$