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.