Fascinated by ocean life, Hannah wants to put a saltwater aquarium in her bedroom. She needs to make sure she buys a big enough tank to grow her collection of fish over time.
This table shows the relationship between the number of fish in Hannah's collection, x, and the smallest tank size (in gallons), y, she needs to safely keep her fish.
x (fish) y (gallons)
2 18
7 63
8 72
10 90
According to the values in the table, do x and y have a proportional relationship?
To determine if x and y have a proportional relationship, we need to check if the ratio of y to x is the same for all data points.
For example, for the first data point, when x=2 and y=18, y/x = 18/2 = 9.
For the second data point, when x=7 and y=63, y/x = 63/7 = 9.
For the third data point, when x=8 and y=72, y/x = 72/8 = 9.
For the fourth data point, when x=10 and y=90, y/x = 90/10 = 9.
Since the ratio of y to x is the same (9) for all data points, we can conclude that x and y have a proportional relationship.