To determine if the table represents a linear function, we need to check if the rate of change between $x$ and $y$ is constant. For a function to be linear, the difference in $y$-values divided by the difference in $x$-values (i.e., the slope) should be the same between each pair of points.

The table provided has the following points:

• (0, 25)
• (7, 20)
• (14, 15)
• (21, 10)

Let's calculate the change in $y$ for each step of $x$:

1. From $(0, 25)$ to $(7, 20)$: $\text{Change in } y = 20 - 25 = -5 \quad \text{and change in } x = 7 - 0 = 7$ Slope = $\frac{-5}{7}$.

2. From $(7, 20)$ to $(14, 15)$: $\text{Change in } y = 15 - 20 = -5 \quad \text{and change in } x = 14 - 7 = 7$ Slope = $\frac{-5}{7}$.

3. From $(14, 15)$ to $(21, 10)$: $\text{Change in } y = 10 - 15 = -5 \quad \text{and change in } x = 21 - 14 = 7$ Slope = $\frac{-5}{7}$.

Since the slope remains constant at $\frac{-5}{7}$ between each pair of points, this indicates that the relationship between $x$ and $y$ is linear.

Answer: The table represents a linear function.

Would you like more details or have any questions?

Here are some additional questions that expand on this topic:

1. What is the equation of the linear function represented by this table?
2. How can you determine if a function is nonlinear using a table of values?
3. What is the significance of a constant slope in identifying a linear function?
4. How would the answer change if one of the slopes was different?
5. Can you think of real-life examples where linear relationships are useful?

Tip: When examining a table, look for a constant rate of change in $y$ with respect to $x$ to quickly identify linear relationships.