Fascinated by ocean life, Trent wants to put a saltwater aquarium in his bedroom. He needs to make sure he buys a big enough tank to grow his collection of fish over time.

To determine if \( x \) (the number of fish) and \( y \) (the tank size in gallons) have a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for the values given in the table.

Let's calculate the ratios for each pair:

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 \( \frac{y}{x} \) is consistently 17 for all values of \( x \), \( x \) and \( y \) do have a proportional relationship.

Answer:

Yes, they have a proportional relationship. The constant of proportionality is 17.