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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.

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

Learn how to determine if a function is linear or nonlinear by analyzing a table of values and calculating the rate of change. This problem covers core algebraic concepts and uses the slope formula to decide if the rate of change is constant or variable. Suitable for students in Grades 6-8.

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