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The problem asks for the **constant of proportionality** \( r \) in the equation \( y = r \cdot x \). Let's walk through the solution:

From the table provided:
- When \( x = 5.8 \), \( y = 5.8 \)
- When \( x = 7.5 \), \( y = 7.5 \)
- When \( x = 11.2 \), \( y = 11.2 \)

Since the values of \( y \) are equal to the values of \( x \) for all entries in the table, this suggests that:
\[
r = \frac{y}{x}
\]
If we plug in any pair from the table:
\[
r = \frac{5.8}{5.8} = 1
\]
or using another entry:
\[
r = \frac{7.5}{7.5} = 1
\]

Thus, the **constant of proportionality \( r \)** is:
\[
r = 1
\]

This tells us that for every \( x \), the corresponding \( y \) is simply \( y = 1 \cdot x \), meaning \( y = x \).

---

Would you like any further explanation or examples?  

Here are 5 follow-up questions that can expand your understanding:  
1. What happens if the constant of proportionality \( r \) is not 1?  
2. How does the graph of \( y = r \cdot x \) look when \( r = 1 \)?  
3. If the table had \( y = 2x \) instead, what would the new \( r \) be?  
4. What is the difference between a direct proportion and a linear function?  
5. Can the constant \( r \) ever be negative? If yes, what would that mean?

**Tip:** Whenever two variables are proportional, the ratio between them remains constant across all values.

Find the constant of proportionality (r) in the equation y = rx from the table where x and y are proportional.

Learn how to find the constant of proportionality (r) in the equation y = rx from a table where x and y are proportional. This problem covers key mathematical concepts such as proportionality and ratios, suitable for students in Grades 6-8.

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