Question

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.
This table shows the relationship between the number of fish in Trent's collection, x, and the smallest tank size (in gallons), y, he needs to safely keep his fish.
x (fish) y (gallons)
1 17
2 34
3 51
5 85
According to the values in the table, do x and y have a proportional relationship?
yes
no

Answer 1

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

Calculating the ratios for the provided values:

1. For \( x = 1 \):
\[
\frac{y}{x} = \frac{17}{1} = 17
\]

2. For \( x = 2 \):
\[
\frac{y}{x} = \frac{34}{2} = 17
\]

3. For \( x = 3 \):
\[
\frac{y}{x} = \frac{51}{3} = 17
\]

4. For \( x = 5 \):
\[
\frac{y}{x} = \frac{85}{5} = 17
\]

Since the ratio \( \frac{y}{x} \) is constantly \( 17 \) for all the pairs of values, we can conclude that \( x \) and \( y \) do indeed have a proportional relationship.

Therefore, the answer is:
**yes**