Question

for the function $f(x)=x^{2}-10$, find the slope of the secant line between $x = - 5$ and $x = 4$.

Explanation:

Step1: Find \( f(-5) \) and \( f(4) \)

For \( x=-5 \), \( f(-5)=(-5)^{2}-10=25 - 10=15 \).
For \( x = 4 \), \( f(4)=4^{2}-10=16 - 10 = 6 \).

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

Here \( x_1=-5 \), \( x_2 = 4 \), \( f(x_1)=15 \), \( f(x_2)=6 \).
\( m=\frac{6 - 15}{4-(-5)}=\frac{-9}{9}=-1 \).

Answer:

\(-1\)