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To determine if the relationship between \( x \) and \( y \) in the table is proportional, we need to check if there is a constant ratio \( \frac{y}{x} \) for each pair of values. If this ratio remains the same across all pairs, then \( y \) is proportional to \( x \) and the equation \( y = kx \) can be written, where \( k \) is the constant of proportionality.

Let's examine each pair in the table:

1. For \( x = 5 \), \( y = 15 \):
   \[
   \frac{y}{x} = \frac{15}{5} = 3
   \]

2. For \( x = 6 \), \( y = 18 \):
   \[
   \frac{y}{x} = \frac{18}{6} = 3
   \]

3. For \( x = 7 \), \( y = 21 \):
   \[
   \frac{y}{x} = \frac{21}{7} = 3
   \]

4. For \( x = 8 \), \( y = 24 \):
   \[
   \frac{y}{x} = \frac{24}{8} = 3
   \]

Since the ratio \( \frac{y}{x} = 3 \) is constant for each pair, the relationship is indeed proportional, with the constant of proportionality \( k = 3 \).

Thus, the equation that relates \( y \) to \( x \) is:
\[
y = 3x
\]

**Correct Answer:** Yes; \( y = 3x \)

Would you like a deeper explanation, or do you have any questions?

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### Related Questions:
1. How can you determine if a table shows a proportional relationship without calculating each ratio?
2. What is the significance of the constant of proportionality in a proportional relationship?
3. How would the table look if \( y = 5x \) instead of \( y = 3x \)?
4. Can a table with a proportional relationship ever have negative values for \( x \) and \( y \)?
5. How does a proportional relationship differ from a linear relationship?

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### Tip:
In proportional relationships, both variables change at a constant rate relative to each other, resulting in a straight line that passes through the origin when graphed.

Is the given table a proportional relationship? If so, write an equation that relates y to x.

Learn how to determine if a table of values represents a proportional relationship and how to write an equation that relates y to x. This problem involves calculating ratios and identifying the constant of proportionality. Suitable for students in Grades 6-8.

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