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.
(1 point)
Responses
Yes, the ratios are in a proportional relationship.
Yes, the ratios are in a proportional relationship.
No, the ratio of 1 hour to $9 is not proportional.
No, the ratio of 1 hour to $9 is not proportional.
No, the ratios are not equivalent.
No, the ratios are not equivalent.
No, the ratio of 3 hours to $27 is not proportional.
No, the ratios are not equivalent.
To determine if the quantities in the data table are in a proportional relationship, we can check if the ratios are equivalent.
Let's calculate the ratios for each set of hours and money:
For the first set (1 hour, $9), the ratio is 1:9.
For the second set (2 hours, $18), the ratio is 2:18, which simplifies to 1:9.
For the third set (3 hours, $27), the ratio is 3:27, which simplifies to 1:9.
For the fourth set (4 hours, $36), the ratio is 4:36, which simplifies to 1:9.
Since all the ratios are equivalent (all simplified to 1:9), we can conclude that the quantities in the data table are in a proportional relationship.
Therefore, the answer is: Yes, the ratios 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 of hours to money is consistent across all the data points.
Let's calculate the ratio of hours to money for each data point:
- For 1 hour, the ratio of hours to money is 1:9.
- For 2 hours, the ratio of hours to money is 2:18, which simplifies to 1:9.
- For 3 hours, the ratio of hours to money is 3:27, which simplifies to 1:9.
- For 4 hours, the ratio of hours to money is 4:36, which simplifies to 1:9.
Since the ratio of hours to money is consistent at 1:9 across all data points, we can conclude that the quantities in the data table are indeed in a proportional relationship.
Therefore, the correct response is:
Yes, the ratios are in a proportional relationship.