https://file.aiquickdraw.com/mathbot/file/1727722067537qvyg6kks.jpg

To determine if the table is proportional or non-proportional, we need to check if the ratio between corresponding values of \( x \) and \( y \) remains constant. Let's calculate the ratios for each pair of \( x \) and \( y \):

1. For \( x = -9 \), \( y = 13.5 \):
   \[
   \text{Ratio} = \frac{y}{x} = \frac{13.5}{-9} = -1.5
   \]

2. For \( x = -8 \), \( y = 12 \):
   \[
   \text{Ratio} = \frac{y}{x} = \frac{12}{-8} = -1.5
   \]

3. For \( x = -7 \), \( y = 10.5 \):
   \[
   \text{Ratio} = \frac{y}{x} = \frac{10.5}{-7} = -1.5
   \]

4. For \( x = -6 \), \( y = 9 \):
   \[
   \text{Ratio} = \frac{y}{x} = \frac{9}{-6} = -1.5
   \]

Since the ratio \( \frac{y}{x} \) is constant for all pairs of \( x \) and \( y \), the table represents a proportional relationship.

### Conclusion:
The table is **proportional**.

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Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How can you recognize a proportional relationship in a table?
2. How do you write the equation of a proportional relationship?
3. What is the constant of proportionality in this table?
4. How would the table look if the relationship were non-proportional?
5. Can you graph the values from the table to verify proportionality?

**Tip:** A proportional relationship always passes through the origin when graphed.

Is the table proportional or non-proportional?

Learn how to determine if a table represents a proportional relationship by calculating and checking constant ratios between x and y. This table, where the ratios remain constant, represents a proportional relationship. Suitable for students in Grades 6-8.

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