Find and compare the slope between each pair of points. What does it mean if any of the slopes are different?
Linear? No, see solution.
Practice makes perfect
One way to determine if points are collinear is to calculate and compare the slope 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 one other point in the data set.
Rate of Change Between...
y_2-y_1/x_2-x_1
m
( 1, 18)&( 2, 15)
15- 18/2- 1
-3
( 2, 15)&( 4, 12)
12- 15/4- 2
-3/2
( 4, 12)&( 8, 9)
9- 12/8- 4
-3/4
We see that the slope between each pair of points is different. Since the rate of change is inconsistent, we know that the points are not collinear. Therefore, it is also not possible to write a linear equation that represents y as a function of x.
