Question

for the function ( f(x)=x^{2}-8 ), find the slope of the secant line between ( x = - 1 ) and ( x = 2 ).

Explanation:

Step1: Find \( f(-1) \) and \( f(2) \)

Substitute \( x=-1 \) into \( f(x)=x^{2}-8 \): \( f(-1)=(-1)^{2}-8=1 - 8=-7 \)
Substitute \( x = 2 \) into \( f(x)=x^{2}-8 \): \( f(2)=2^{2}-8=4 - 8=-4 \)

Step2: Use the slope formula for the secant line

The slope formula for the secant line between two points \( (x_1,f(x_1)) \) and \( (x_2,f(x_2)) \) is \( m=\frac{f(x_2)-f(x_1)}{x_2 - x_1} \)
Here \( x_1=-1,x_2 = 2,f(x_1)=-7,f(x_2)=-4 \)
\( m=\frac{-4-(-7)}{2-(-1)}=\frac{-4 + 7}{2 + 1}=\frac{3}{3}=1 \)

Answer:

\(1\)