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To help you solve this, the problem involves checking whether the number of fish \( x \) and the corresponding number of gallons \( y \) in the table form a proportional relationship.

The table you provided shows:

\[
\begin{array}{c|c}
\text{x (fish)} & \text{y (gallons)} \\
\hline
1 & 17 \\
2 & 34 \\
3 & 51 \\
5 & 85 \\
\end{array}
\]

### Proportional Relationship Check
In a proportional relationship, the ratio \(\frac{y}{x}\) should be constant for all pairs of \(x\) and \(y\).

1. For \(x = 1\), \(y = 17\): \(\frac{y}{x} = \frac{17}{1} = 17\)
2. For \(x = 2\), \(y = 34\): \(\frac{y}{x} = \frac{34}{2} = 17\)
3. For \(x = 3\), \(y = 51\): \(\frac{y}{x} = \frac{51}{3} = 17\)
4. For \(x = 5\), \(y = 85\): \(\frac{y}{x} = \frac{85}{5} = 17\)

Since the ratio is always 17, the number of gallons per fish is constant. This means that \(x\) and \(y\) do have a proportional relationship, with the constant of proportionality being 17 gallons per fish.

Would you like further explanation or have any specific questions? Here are some related questions to deepen your understanding:

1. How would you write an equation for the relationship between \(x\) and \(y\)?
2. What does the constant of proportionality represent in real life?
3. Can you predict how many gallons would be needed for 10 fish?
4. Is the proportional relationship always linear, and why?
5. How does this concept apply to other real-life examples, like cost per item?

**Tip:** When checking for proportionality, always calculate the ratio for each pair of values. If the ratio remains constant, the relationship is proportional!

According to the values in the table, do x (fish) and y (gallons) have a proportional relationship? What is the constant of proportionality? Write your answer as a whole number or decimal.

Learn how to determine if the number of fish and gallons in a tank have a proportional relationship using a table of values. Calculate the constant of proportionality and understand the concept of proportionality in real-life contexts, suitable for Grades 6-8.

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