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 trents collection, x, and the smallest tank size (in gallons), y, he needs to safely keep his fish.

x (fish)	y (gallons)
2	34
3	51
5	85

according to the values in the table, do x and y have a proportional relationship? yes no

Explanation:

Step1: Calculate the ratio for each pair

For the first pair ($x = 1,y = 17$), the ratio $\frac{y}{x}=\frac{17}{1}=17$.
For the second pair ($x = 2,y = 34$), the ratio $\frac{y}{x}=\frac{34}{2}=17$.
For the third pair ($x = 3,y = 51$), the ratio $\frac{y}{x}=\frac{51}{3}=17$.
For the fourth pair ($x = 5,y = 85$), the ratio $\frac{y}{x}=\frac{85}{5}=17$.

Step2: Check the constancy of the ratio

Since the ratio $\frac{y}{x}$ is a constant value (17) for all pairs in the table, $x$ and $y$ have a proportional relationship.

Answer:

yes