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The table provided shows a proportional relationship between \( x \) and \( y \). To find the constant of proportionality, we use the formula:

\[
k = \frac{y}{x}
\]

For the values in the table:
- When \( x = 2 \) and \( y = 3 \):

\[
k = \frac{3}{2} = 1.5
\]

- When \( x = 6 \) and \( y = 9 \):

\[
k = \frac{9}{6} = 1.5
\]

Since the ratio \( \frac{y}{x} \) is consistent for both pairs of values, the constant of proportionality is \( k = 1.5 \), which matches the answer choice \( \frac{3}{2} \).

Thus, the correct answer is:
\[
\boxed{\frac{3}{2}}
\]

Would you like more details or have any further questions?

Here are 5 related questions to practice:
1. How do you verify if a table represents a proportional relationship?
2. What happens if the constant of proportionality is less than 1?
3. How can the constant of proportionality be used in word problems?
4. What is the relationship between the slope of a line and proportional relationships?
5. Can two variables have a proportional relationship if one of the values is zero?

**Tip:** The constant of proportionality is the same as the slope in a linear equation \( y = kx \) when the line passes through the origin.

The table above shows a proportional relationship. What is the constant of proportionality?

Learn how to find the constant of proportionality from a table of values showing the relationship between two variables, x and y. This solution involves the use of ratios and proportionality, suitable for students in Grades 6-8.

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