Proportional Relationships in Tables Quick Check
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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 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.
No, the ratio of 1 hour to $9 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 the hours and the money remain constant.
Let's calculate the ratios for each pair of values in the table:
- The ratio of 1 hour to $9 is 1/9.
- The ratio of 2 hours to $18 is 2/18 = 1/9.
- The ratio of 3 hours to $27 is 3/27 = 1/9.
- The ratio of 4 hours to $36 is 4/36 = 1/9.
As we can see, the ratios are all equal to 1/9, so the quantities in the data table are in a proportional relationship.
Therefore, the correct response is:
Yes, the ratios are in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of hours to money ($), for each row, are equivalent.
Let's calculate the ratios:
For the first row:
Ratio of hours to money = 1 hour / $9 = 1/9
For the second row:
Ratio of hours to money = 2 hours / $18 = 2/18 = 1/9
For the third row:
Ratio of hours to money = 3 hours / $27 = 3/27 = 1/9
For the fourth row:
Ratio of hours to money = 4 hours / $36 = 4/36 = 1/9
Since all the ratios are equal to 1/9, we can conclude that the quantities in the data table are in a proportional relationship.
Therefore, the correct response is: Yes, the ratios are in a proportional relationship.