https://file.aiquickdraw.com/mathbot/file/1729887967817caxtfb5y.jpg

Let's examine the tables and check whether \( x \) and \( y \) are proportional.

### Table 1:
We check if there is a constant ratio between \( y \) and \( x \) in all pairs.

For each pair:
\[
\frac{y}{x} = \frac{2}{14} = \frac{1}{7}, \quad \frac{3}{21} = \frac{1}{7}, \quad \frac{5}{35} = \frac{1}{7}, \quad \frac{56}{8} = 7
\]

The ratios are not constant because \( \frac{y}{x} = 7 \) in the last case, while the others give \( \frac{y}{x} = \frac{1}{7} \). Therefore, **Table 1 is not proportional**.

### Table 2:
We repeat the process for Table 2:

For each pair:
\[
\frac{y}{x} = \frac{6}{2} = 3, \quad \frac{12}{3} = 4, \quad \frac{25}{5} = 5, \quad \frac{48}{8} = 6
\]

Here, the ratios are not constant either. Therefore, **Table 2 is not proportional**.

In conclusion:
- **Table 1: Not proportional**
- **Table 2: Not proportional**

Would you like more details on this or have any other questions? Here are some related questions for further exploration:

1. What defines a proportional relationship between two variables?
2. How can we calculate the constant of proportionality when it exists?
3. Can proportionality exist if the relationship is inverse (e.g., \( y = \frac{k}{x} \))?
4. How does a proportional graph differ from a non-proportional graph?
5. What are some real-life examples of proportional relationships?

**Tip:** Always check for a consistent ratio between corresponding values to determine proportionality.

For each table, determine whether it shows that x and y are proportional. If x and y are proportional, fill in the blank with a number in simplest form.

Analyze two tables to check if x and y values are proportional by calculating the ratio between corresponding values. Identify whether the relationship holds constant for each table and solve for the constant of proportionality when it exists. Suitable for students in Grades 6-8.

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