Hours Money ($)

Question

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.

Answer 1

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

Let's calculate the ratios for each pair:

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 equal (all equal to 9), the amounts of money are directly proportional to the number of hours.

Therefore, the correct response is:

Yes, the ratios are in a proportional relationship.