Chapter 3.3, Problem 24E

When Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the data are linear. But if data not evenly spaced, then we must calculate the average rate of change over each interval to see whether the data are linear. If the average rate of changes is constant, it is the slope of the linear function. This fact is used in Exercises 23 and 24.

In the following table, show that the average rate of change is the same over each interval. This shows the data are linear, even though the differences in $y$ are not constant. Then find a linear model for the data.

$\mathit{x}$	$1$	$2$	$5$	$6$
$\mathit{y}$	$7$	$10$	$19$	$22$