Use the table to answer the question.
Hours Money ($)
1 9
2 18
3 27
4 36
Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
The quantities in the data table are in a proportional relationship. This is because the value of money ($9) increases by a constant factor of 9 for every hour increase (1 hour). Therefore, as the number of hours increases, the amount of money increases proportionally.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio of the Money to the Hours is constant.
Let's calculate the ratio for each pair of values:
For Hours 1 and 2: Money ($18) / Hours (2) = 9
For Hours 2 and 3: Money ($27) / Hours (3) = 9
For Hours 3 and 4: Money ($36) / Hours (4) = 9
Since the ratio is constant in all cases, we can conclude that the quantities in the data table are in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio between hours and money remains constant. We can calculate the ratio between hours and money for each data point:
For the first data point: 1 hour / $9 = 1/9
For the second data point: 2 hours / $18 = 2/18 = 1/9
For the third data point: 3 hours / $27 = 3/27 = 1/9
For the fourth data point: 4 hours / $36 = 4/36 = 1/9
As we can see, in all cases the ratio is 1/9. Therefore, the quantities in the data table are in a proportional relationship because the ratio between hours and money remains constant.