Exercise 5 Page 177

One way to determine if points are collinear is to calculate and compare the slope, or rate of change, of the line between points in the data set. We can do this by using the Slope Formula. Note that it is enough to check each point with just another point in the data set.

Rate of change between...	$\frac{y _{2} - y _{1}}{x _{2} - x _{1}}$	$m$
$(8, 7)$ & $(12, 5)$	$\frac{5 - 7}{1 2 - 8}$	$- \frac{1}{2}$
$(12, 5)$ & $(16, 3)$	$\frac{3 - 5}{1 6 - 1 2}$	$- \frac{1}{2}$
$(16, 3)$ & $(20, 0)$	$\frac{0 - 3}{2 0 - 1 6}$	$- \frac{3}{4}$
$(20, 0)$ & $(24, - 2)$	$\frac{- 2 - 0}{2 4 - 2 0}$	$- \frac{1}{2}$

We can see that the slope between the points $(16, 3)$ and $(20, 0)$ is $- \frac{3}{4}$ , while every other pair presented in the table has a rate of change equal to $- \frac{1}{2} .$ Since the rate of change is not constant, we know that the function is nonlinear.