Question

for the function $f(x)=x^{2}-8$, find the slope of the secant line between $x = - 5$ and $x = 6$.

Explanation:

Step1: Find \(f(-5)\) and \(f(6)\)

For \(x = - 5\), \(f(-5)=(-5)^{2}-8=25 - 8=17\).
For \(x = 6\), \(f(6)=6^{2}-8=36 - 8 = 28\).

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

Here \(a=-5\), \(b = 6\), \(f(a)=17\), \(f(b)=28\).
\(m=\frac{28 - 17}{6-(-5)}=\frac{11}{6 + 5}\)

Step3: Simplify the fraction

\(m=\frac{11}{11}=1\)

Answer:

\(1\)