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 ratio of 3 hours to $27 is not proportional.
No, the ratios are not equivalent.
No, the ratio of 3 hours to $27 is not proportional.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the hours and money values are equivalent or not.
Let's calculate the ratios:
For 1 hour and $9, the ratio is 1:9
For 2 hours and $18, the ratio is 2:18
For 3 hours and $27, the ratio is 3:27
For 4 hours and $36, the ratio is 4:36
If these ratios are all equivalent (i.e., they reduce to the same fraction), then the quantities are in a proportional relationship.
Calculating the equivalent ratios:
1:9 reduces to 1:9
2:18 reduces to 1:9
3:27 reduces to 1:9
4:36 reduces to 1:9
Since all the ratios are equivalent and reduce to 1:9, we can conclude that the quantities in the data table are in a proportional relationship.
Therefore, the correct response 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 ratios between hours and money remain constant.
To do this, we can find the ratios for each pair of values. For example:
- 1 hour to $9 gives us a ratio of 1:9
- 2 hours to $18 gives us a ratio of 2:18, which simplifies to 1:9
- 3 hours to $27 gives us a ratio of 3:27, which simplifies to 1:9
- 4 hours to $36 gives us a ratio of 4:36, which simplifies to 1:9
Since all the ratios are the same (1:9), the quantities in the data table are indeed in a proportional relationship.
So the correct response would be:
Yes, the ratios are in a proportional relationship.