Question

for the function ( f(x) = x^{2} - 9 ), find the slope of the secant line between ( x = -6 ) and ( x = -2 ).

Explanation:

Step1: Find \( f(-6) \) and \( f(-2) \)

For \( x=-6 \), \( f(-6)=(-6)^{2}-9=36 - 9=27 \).
For \( x = - 2 \), \( f(-2)=(-2)^{2}-9=4 - 9=-5 \).

Step2: Use the slope formula for the secant line \( m=\frac{f(x_2)-f(x_1)}{x_2 - x_1} \)

Here \( x_1=-6 \), \( x_2=-2 \), \( f(x_1) = 27 \), \( f(x_2)=-5 \).
\( m=\frac{-5 - 27}{-2-(-6)}=\frac{-32}{4}=-8 \).

Answer:

\(-8\)