To determine if the function in the table is linear or nonlinear, we need to check whether the rate of change between the values of $x$ and $y$ remains constant.

The table provides the following values:

• When $x = 16$, $y = 19$
• When $x = 17$, $y = 11$
• When $x = 18$, $y = 2$

Now, calculate the rate of change (slope) between consecutive points:

1. Between $(16, 19)$ and $(17, 11)$: $\text{slope} = \frac{11 - 19}{17 - 16} = \frac{-8}{1} = -8$

2. Between $(17, 11)$ and $(18, 2)$: $\text{slope} = \frac{2 - 11}{18 - 17} = \frac{-9}{1} = -9$

Since the slopes $-8$ and $-9$ are not equal, the rate of change is not constant, indicating that the function is nonlinear.

Would you like further details or have any questions?

Here are 5 related questions:

1. What conditions must be met for a function to be considered linear?
2. Can a nonlinear function ever have a constant rate of change for a part of its domain?
3. How can you graphically determine if a function is linear or nonlinear?
4. What is the general form of the equation for a linear function?
5. How does a function’s rate of change affect its graph?

Tip: For a function to be linear, its graph must form a straight line, and its rate of change (slope) must remain constant.