Question

secant lines
1/8 penalty: none
question
for the function ( f(x)=x^{2}+4 ), find the slope of the secant line
between ( x=-2 ) and ( x = 1 ).
answer attempt 1 out of 2

Explanation:

Step1: Recall the formula for the slope of the secant line

The formula for the slope of the secant line between two points \(x = a\) and \(x = b\) on the function \(y = f(x)\) is \(m=\frac{f(b)-f(a)}{b - a}\). Here, \(a=-2\) and \(b = 1\), and \(f(x)=x^{2}+4\).

Step2: Calculate \(f(-2)\) and \(f(1)\)

• For \(x=-2\), \(f(-2)=(-2)^{2}+4=4 + 4=8\).
• For \(x = 1\), \(f(1)=1^{2}+4=1 + 4=5\).

Step3: Substitute into the slope formula

\(m=\frac{f(1)-f(-2)}{1-(-2)}=\frac{5 - 8}{1 + 2}=\frac{-3}{3}=-1\).

Answer:

\(-1\)