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 money
1 9
2 18
3 27
4 36
To determine if the data table represents a proportional relationship, we need to check if the ratio of the money earned to the number of hours worked remains constant.
Let's calculate the ratios for each set of data:
- For 1 hour worked, the money earned is 9 (9/1 = 9/1 = 9).
- For 2 hours worked, the money earned is 18 (18/2 = 9).
- For 3 hours worked, the money earned is 27 (27/3 = 9).
- For 4 hours worked, the money earned is 36 (36/4 = 9).
As we can see, the ratio of money earned to hours worked is consistently 9. This means that for every additional hour worked, the amount of money earned increases by a factor of 9.
Therefore, the data table represents a proportional relationship because the ratio of money earned to hours worked is constant.