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 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.
No, the ratios are not equivalent.
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 are equivalent for all values in the table.
Let's calculate the ratios:
For 1 hour: $9/1 = 9/1 = 9
For 2 hours: $18/2 = 9/1 = 9
For 3 hours: $27/3 = 9/1 = 9
For 4 hours: $36/4 = 9/1 = 9
Since the ratios between hours and money are consistently 9/1 for all values in the table, the quantities in the data table are indeed in a proportional relationship. Therefore, the answer would be:
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 calculate the ratio of each pair of values:
For the first pair, 1 hour to $9:
Ratio = 1 hour / $9 = 1/9.
For the second pair, 2 hours to $18:
Ratio = 2 hours / $18 = 1/9.
For the third pair, 3 hours to $27:
Ratio = 3 hours / $27 = 1/9.
For the fourth pair, 4 hours to $36:
Ratio = 4 hours / $36 = 1/9.
As we can see, the ratio remains constant at 1/9 for all pairs. Therefore, we can conclude that the quantities in the data table are in a proportional relationship.
So, the correct response is:
Yes, the ratios are in a proportional relationship.