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The problem involves recognizing proportional relationships in tables. Let's analyze each table to determine if they represent a proportional relationship and, if they do, identify the constant of proportionality.

### Table 1:
\[
\begin{array}{c|c}
x & y \\
\hline
2 & 18 \\
5 & 45 \\
7 & 63 \\
\end{array}
\]

To determine if the relationship is proportional, divide \( y \) by \( x \) for each pair:

1. \(\frac{y}{x} = \frac{18}{2} = 9\)
2. \(\frac{y}{x} = \frac{45}{5} = 9\)
3. \(\frac{y}{x} = \frac{63}{7} = 9\)

Since the ratio \( \frac{y}{x} \) is constant (always 9), the relationship is proportional. The constant of proportionality is **9**.

### Table 2:
\[
\begin{array}{c|c}
x & y \\
\hline
3 & 42 \\
4 & 60 \\
5 & 80 \\
\end{array}
\]

Let's check if this table represents a proportional relationship by calculating \( \frac{y}{x} \):

1. \(\frac{y}{x} = \frac{42}{3} = 14\)
2. \(\frac{y}{x} = \frac{60}{4} = 15\)
3. \(\frac{y}{x} = \frac{80}{5} = 16\)

The ratio \( \frac{y}{x} \) is not constant (14, 15, and 16), so this table **does not** represent a proportional relationship.

### Summary:
- **Table 1**: Proportional relationship with a constant of proportionality of **9**.
- **Table 2**: Not a proportional relationship.

Would you like more details or have any questions?

Here are 5 related questions:
1. How can you verify if a table represents a proportional relationship?
2. What does the constant of proportionality represent in a real-world scenario?
3. Can a non-linear relationship be proportional?
4. How do changes in \( x \) affect \( y \) in a proportional relationship?
5. What are examples of real-life situations that involve proportional relationships?

**Tip:** When checking for proportionality, always look for a consistent ratio between the two variables across all data points.

Tell whether each table represents a proportional relationship. If it does, identify the constant of proportionality. Table 1: x = [2, 5, 7], y = [18, 45, 63]. Table 2: x = [3, 4, 5], y = [42, 60, 80].

Learn how to identify proportional relationships in tables using ratios. This example problem helps you understand how to calculate and verify the constant of proportionality in two different tables. Ideal for Grade 7 students.

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