# How do you find the average rate of change of y = x^2 + 7x over [1,8]?

Jan 2, 2016

$16$

#### Explanation:

The average rate of change is the slope on that interval.

The slope, or rise over run, measures the change in $y$-values over the change in $x$-values.

The $y$-values are $f \left(1\right)$ and $f \left(8\right)$ and the $x$-values are $1$ and $8$.

Thus, the average rate of change is equal to

$\frac{f \left(1\right) - f \left(8\right)}{1 - 8}$

Find $f \left(1\right)$ and $f \left(8\right)$.

$f \left(1\right) = {1}^{2} + 7 \left(1\right) = 8$

$f \left(8\right) = {8}^{2} + 7 \left(8\right) = 120$

Thus, the average rate of change is equal to

$\frac{8 - 120}{1 - 8} = \frac{- 112}{- 7} = 16$