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To determine if there is a proportional relationship between \( X \) and \( Y \) in this table, we need to check if there is a consistent multiplier (constant of proportionality) between the \( X \) values and \( Y \) values.

The table shows the following pairs:
- When \( X = 2 \), \( Y = 18 \)
- When \( X = 3 \), \( Y = 27 \)
- When \( X = 4 \), \( Y = 36 \)
- When \( X = 6 \), \( Y = 54 \)

For each pair, let's check the ratio \( \frac{Y}{X} \):
- \( \frac{18}{2} = 9 \)
- \( \frac{27}{3} = 9 \)
- \( \frac{36}{4} = 9 \)
- \( \frac{54}{6} = 9 \)

Since the ratio \( \frac{Y}{X} = 9 \) is constant across all pairs, the relationship is proportional. The equation representing this relationship is:
\[
Y = 9X
\]

The correct answer is:
**\( Y = 9X \)**

Would you like further details on this solution or have any questions?

Here are some related questions to deepen understanding:
1. What does it mean for two variables to have a proportional relationship?
2. How can we determine the constant of proportionality between two variables?
3. What would the equation be if the proportionality constant were different, such as 5 instead of 9?
4. How can we use a table of values to check for proportional relationships?
5. How would the graph of a proportional relationship look like?

**Tip:** When given a table of values, calculating the ratio between variables can quickly reveal if the relationship is proportional.

If the relationship in the table is proportional, write its equation.

Identify if a relationship in a table is proportional and write its equation. This example shows how to find the constant of proportionality, k, and use it to form the equation y = kx. Suitable for Grade 7 students learning about proportional relationships.

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