Question

decide whether the following statement is true or false.
the slope of a nonvertical line is the average rate of change of the linear function.

choose the correct answer below

false

true

Explanation:

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([x_1,x_2]\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). For a linear function \(y=mx + b\), \(f(x_1)=mx_1 + b\) and \(f(x_2)=mx_2 + b\). Then \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{(mx_2 + b)-(mx_1 + b)}{x_2 - x_1}=\frac{m(x_2 - x_1)}{x_2 - x_1}=m\), where \(m\) is the slope of the non - vertical line \(y = mx + b\).

Answer:

True