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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.

Does the table represent a linear function or a nonlinear function?

Learn how to determine if a table of values represents a linear function by calculating the rate of change between x and y values. This example, featuring a constant slope of -5/7, illustrates key concepts in algebra and linear functions. Ideal for students in Grades 6-8.

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