To determine the constant of proportionality between $x$ and $y$, we need to check if the relationship between $x$ and $y$ is proportional. A proportional relationship is one in which $y$ is directly proportional to $x$, meaning the ratio $\frac{y}{x}$ is constant.

Let's calculate the ratio $\frac{y}{x}$ for each pair of values in the table:

1. For $x = 3$ and $y = 24$: $\frac{y}{x} = \frac{24}{3} = 8$

2. For $x = 7$ and $y = 56$: $\frac{y}{x} = \frac{56}{7} = 8$

3. For $x = 11$ and $y = 88$: $\frac{y}{x} = \frac{88}{11} = 8$

4. For $x = 15$ and $y = 120$: $\frac{y}{x} = \frac{120}{15} = 8$

Since the ratio $\frac{y}{x}$ is constant and equal to 8 for all values of $x$, the constant of proportionality is 8.

Would you like more details on how this works or have any questions?

Here are 5 related questions:

1. How can you use the constant of proportionality to predict $y$ for any given $x$?
2. How does the concept of proportionality relate to linear equations?
3. What happens if the relationship between $x$ and $y$ is not proportional?
4. Can you have a proportional relationship if one of the values of $x$ is 0?
5. How do you determine proportionality from a graph?

Tip: In a proportional relationship, the graph of $y$ vs. $x$ will always be a straight line passing through the origin.