To identify the constant of proportionality from the table, we need to check if there is a direct proportional relationship between $x$ and $y$. In such a case, $y$ is proportional to $x$ according to the formula:

$y = kx$

where $k$ is the constant of proportionality. To find $k$, we calculate $\frac{y}{x}$ for each pair of $x$ and $y$ values from the table.

From the table:

• For $x = 2$ and $y = 18$, $\frac{y}{x} = \frac{18}{2} = 9$
• For $x = 5$ and $y = 45$, $\frac{y}{x} = \frac{45}{5} = 9$
• For $x = 7$ and $y = 63$, $\frac{y}{x} = \frac{63}{7} = 9$
• For $x = 8$ and $y = 72$, $\frac{y}{x} = \frac{72}{8} = 9$

Since $\frac{y}{x} = 9$ in all cases, the constant of proportionality is:

$k = 9$

Would you like further details, or have any questions?

Here are five related questions:

1. What is the formula used to calculate the constant of proportionality?
2. How can you verify if two variables are proportional from a table?
3. What would the value of $y$ be if $x = 10$?
4. How does the constant of proportionality help in graphing the relationship between $x$ and $y$?
5. What are some real-life examples where proportional relationships are used?

Tip: When two variables are directly proportional, their ratio remains constant across all data points.