The table shows a function. Is the function linear or nonlinear?

x y
-1/2 10
4 8 1/5
8 1/2 -9 4/5

1 answer

To determine if the function is linear or nonlinear, we need to check if the rate of change (slope) is constant.

Let's calculate the slope between the first two points:

slope = (8 1/5 - 10) / (4 - (-1/2)) = -3/3.5

Now let's calculate the slope between the last two points:

slope = (-9 4/5 - 8 1/5) / (8 1/2 - 4) = -18/17

Since the slopes are not equal, the function is nonlinear.