Beginning Algebra With Applications, Chapter 5, 5.1, Section 5.1, Problem 28

$\begin{array}{c|cccc} \text{Month of pregnancy} & 2 & 4 & 6 & 8 \\ \hline\\ \text{Length, in inches} & 1 & 7 & 12 & 16 \end{array}$

Which of the following fractions is the correct one to use to find the average rate of change per month in the length of a fetus from the fourth month of pregnancy to the eighth month of pregnancy?

a. $\displaystyle \frac{4-8}{16-7}$

b. $\displaystyle \frac{16-7}{8-4}$

c. $\displaystyle \frac{8-4}{16-7}$

d. $\displaystyle \frac{7-16}{14-8}$

Average rate of change is the slope of the graph, which is given by rise over run where rise is the rise in y-coordinate and run is the difference in $x$-coordinate. In this case, the $x$-coordinate is the month of pregnancy because it is the independent variable. On the other hand, the $y$-coordinate is the length of the fetus because it is a dependable variable. Based from the table, we have c. $\displaystyle \frac{8-4}{16-7}$.