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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.

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.

1 answer

To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of hours to money are equivalent.

Let's calculate the ratio (money per hour) for each entry in the table:

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

Since all the ratios are equivalent (all equal to 9), the quantities in the data table are in a proportional relationship.

The correct response is: Yes, the ratios are in a proportional relationship.