To determine which of the four relationships has a constant of proportionality of $\frac{1}{3}$, we need to understand that for two variables to be proportional, they must satisfy the equation:

$y = kx$

where $k$ is the constant of proportionality.

The relationship you are looking for would have the form:

$y = \frac{1}{3}x$

If you provide the four relationships, I can identify which one has this constant of proportionality.

Would you like to share the relationships?

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Here are five questions to further explore the concept of proportionality:

1. What is the meaning of the constant of proportionality in a relationship?
2. How does the constant of proportionality affect the slope of a line in a graph?
3. Can the constant of proportionality be negative? What would that signify?
4. What happens if the constant of proportionality is 1? How does it change the relationship?
5. How do you calculate the constant of proportionality from a set of data points?

Tip: In direct proportionality, as one variable increases, the other increases by a consistent factor determined by the constant.