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To find the constant of proportionality \( k \), we can use the formula:

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

This constant should remain the same for each pair of values in the table.

Let's calculate it for each pair of \( x \) and \( y \) values:

- For \( x = 4 \) and \( y = 18 \):
  \[
  k = \frac{18}{4} = 4.5
  \]

- For \( x = 5 \) and \( y = 22.5 \):
  \[
  k = \frac{22.5}{5} = 4.5
  \]

- For \( x = 6 \) and \( y = 27 \):
  \[
  k = \frac{27}{6} = 4.5
  \]

- For \( x = 7 \) and \( y = 31.5 \):
  \[
  k = \frac{31.5}{7} = 4.5
  \]

Since the constant \( k \) is the same for all pairs, the constant of proportionality is \( k = 4.5 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How can you identify a proportional relationship from a table of values?
2. What is the significance of the constant of proportionality in a real-world context?
3. How do we apply the concept of constant proportionality in equations?
4. Can the constant of proportionality change in different contexts or remain fixed?
5. How would you verify proportionality if the values weren't exact?

**Tip**: A quick way to verify if two quantities are proportional is by checking if the ratio \( \frac{y}{x} \) is constant across all pairs of values.

Find the constant of proportionality for the table of values: x = [4, 5, 6, 7] and y = [18, 22.5, 27, 31.5].

Learn how to calculate the constant of proportionality (k) from a table of values. Using the formula k = y / x, we solve for each value pair in the table. The values of x are [4, 5, 6, 7] and the corresponding y-values are [18, 22.5, 27, 31.5]. This problem is suitable for students in Grades 6-8.

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