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 3 hours to $27 is not proportional.
No, the ratio of 3 hours to $27 is not proportional.

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.

1 answer

To determine if the quantities in the given data table are in a proportional relationship, we can examine the ratios of hours to money.

The ratios from the table are:

  • For 1 hour and $9: \( \frac{1}{9} \)
  • For 2 hours and $18: \( \frac{2}{18} = \frac{1}{9} \)
  • For 3 hours and $27: \( \frac{3}{27} = \frac{1}{9} \)
  • For 4 hours and $36: \( \frac{4}{36} = \frac{1}{9} \)

Since all the ratios simplify to \( \frac{1}{9} \), they are equivalent.

Thus, the correct response is:

Yes, the ratios are in a proportional relationship.