Question

is the function described by the points in this table linear or nonlinear?
linear
nonlinear

x	y
-3	9
-1	1
0	0
1	1
3	9

Explanation:

Step1: Recall linear function property

A linear function has a constant rate of change (slope), calculated as $\frac{y_2 - y_1}{x_2 - x_1}$ between any two points.

Step2: Calculate slopes between points

• Between $(-3, 9)$ and $(-1, 1)$: $\frac{1 - 9}{-1 - (-3)} = \frac{-8}{2} = -4$
• Between $(-1, 1)$ and $(0, 0)$: $\frac{0 - 1}{0 - (-1)} = \frac{-1}{1} = -1$
• The slopes are not equal ($-4

eq -1$), so the rate of change is not constant.

Answer:

nonlinear