Question

The quantities in the data table are in a proportional relationship. Using the data in the table, show your work and explain how you know the table represents a proportional relationship.

Hours: 1, 2, 3, 4
Money: 9, 18, 27, 36

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if the table represents a proportional relationship, we need to check if the ratio of money to hours is constant throughout the table.

Let's calculate the ratio for each pair of values:
- For the first pair (1 hour and 9 money): 9/1 = 9
- For the second pair (2 hours and 18 money): 18/2 = 9
- For the third pair (3 hours and 27 money): 27/3 = 9
- For the fourth pair (4 hours and 36 money): 36/4 = 9

As we can see, the ratio of money to hours is consistently 9 in each case. This means that the table represents a proportional relationship where for every hour, the amount of money is 9 times that hour.

In other words, for every additional hour, the amount of money increases by 9 units. This consistent increase shows that the quantities in the data table are in a proportional relationship.