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To determine if the table is proportional, we need to check if the ratio of \( \frac{y}{x} \) remains constant for each pair of \( (x, y) \) values.

The given values are:

\[
\begin{aligned}
x: & \ 1, \ 4, \ 7 \\
y: & \ 3, \ 12, \ 21 \\
\end{aligned}
\]

Let's calculate \( \frac{y}{x} \) for each pair:

1. For \( (1, 3) \): 
   \[
   \frac{y}{x} = \frac{3}{1} = 3
   \]
2. For \( (4, 12) \): 
   \[
   \frac{y}{x} = \frac{12}{4} = 3
   \]
3. For \( (7, 21) \):
   \[
   \frac{y}{x} = \frac{21}{7} = 3
   \]

Since all the ratios are equal (3), the table is **proportional**.

Would you like more details or further clarifications?

Here are 5 related questions:
1. What does it mean for two quantities to be proportional?
2. How can you identify the constant of proportionality in a table?
3. Can a table be proportional if the ratios are not equal?
4. What is the formula for direct proportionality between two variables?
5. How do changes in the values of \( x \) and \( y \) affect proportionality?

**Tip:** Always check if the ratio between corresponding values is constant to determine if the relationship is proportional.

This problem demonstrates how to check if a table is proportional by calculating and comparing the ratios of corresponding values. For each pair of (x, y) values, ensure the ratio y/x remains constant. Suitable for students in Grades 6-8.

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