Question
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
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 ratio of 3 hours to $27 is not proportional.
Yes, the ratios are in a proportional relationship.
No, the ratios are not in a proportional relationship.
No, the ratios are not in a proportional relationship.
The ratio of 1 hour to $9 is not equivalent to the ratio of 2 hours to $18, and the ratio of 3 hours to $27 is also not equivalent to the previous ratios. In a proportional relationship, the ratios between each set of quantities should be equivalent, but in this case, they are not. Therefore, the quantities in the data table are not 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 the hours and money values are equivalent.
Let's calculate the ratios for each data point:
For 1 hour: 9/1 = 9
For 2 hours: 18/2 = 9
For 3 hours: 27/3 = 9
For 4 hours: 36/4 = 9
As we can see, all the ratios are equal to 9. Therefore, the quantities in the data table are in a proportional relationship because the ratios are equivalent.
So, the correct response is:
"Yes, the ratios are in a proportional relationship."