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To determine if the function is linear, we need to check if there is a constant rate of change between the values of \( x \) and \( y \). Let's calculate the change in \( y \) (denoted as \( \Delta y \)) and the change in \( x \) (denoted as \( \Delta x \)) between consecutive points:

1. **Between the first and second rows:**
   \[
   \Delta x = 6 - 1 = 5
   \]
   \[
   \Delta y = 13 - 11 = 2
   \]

   The rate of change is:
   \[
   \frac{\Delta y}{\Delta x} = \frac{2}{5}
   \]

2. **Between the second and third rows:**
   \[
   \Delta x = 11 - 6 = 5
   \]
   \[
   \Delta y = 20 - 13 = 7
   \]

   The rate of change is:
   \[
   \frac{\Delta y}{\Delta x} = \frac{7}{5}
   \]

Since the rate of change is not consistent (it changes from \( \frac{2}{5} \) to \( \frac{7}{5} \)), the function is **nonlinear**.

Would you like more details or have any questions?

Here are 5 related questions:

1. How can you tell if a function is linear just by looking at its graph?
2. What is the general form of a linear function?
3. How can you determine the slope of a linear function from a table?
4. What does it mean for a function to be nonlinear?
5. How would you describe a function that has a consistent rate of change?

**Tip:** For a function to be linear, the rate of change (or slope) must be constant for all intervals.

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

Learn how to determine if a function is linear or nonlinear using a table of values. This problem involves checking if the rate of change between x and y is constant, with a detailed step-by-step solution. Suitable for students in Grades 6-8.

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