To find the constant of proportionality for this relationship, we can use the fact that in a proportional relationship, the ratio between $y$ and $x$ is constant. The formula for the constant of proportionality $k$ is:

$k = \frac{y}{x}$

Let's calculate this ratio using a pair of corresponding values for $x$ and $y$.

From the table:

• When $x = 3$, $y = 4.5$: $k = \frac{4.5}{3} = 1.5$

• When $x = 5$, $y = 7.5$: $k = \frac{7.5}{5} = 1.5$

• When $x = 7$, $y = 10.5$: $k = \frac{10.5}{7} = 1.5$

• When $x = 11$, $y = 16.5$: $k = \frac{16.5}{11} = 1.5$

Since the ratio is consistent in all cases, the constant of proportionality is $k = 1.5$, which equals $\frac{3}{2}$.

Thus, the correct answer is:

$\boxed{\frac{3}{2}}$

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How do you recognize a proportional relationship from a table?
2. Can a proportional relationship have a negative constant of proportionality?
3. How would the table change if the constant of proportionality were $\frac{2}{3}$?
4. How does the graph of a proportional relationship look?
5. What is the formula for a proportional relationship, and how does the constant appear in it?

Tip: In a proportional relationship, you can always find the constant of proportionality by dividing $y$ by $x$, and it should remain the same for all pairs.