Use the table to answer the question.
Hours Biked Miles Traveled
1 12
2 26
3 30
4 48
Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship, indicate why.
(1 point)
Responses
No, not all of the ratios are proportional or have equivalence.
No, not all of the ratios are proportional or have equivalence.
No, you can’t bike 12 miles in an hour.
No, you can’t bike 12 miles in an hour.
Yes, this data table has a proportional relationship.
Yes, this data table has a proportional relationship.
No, none of the ratios have equivalence.
No, not all of the ratios are proportional or have equivalence.
To determine if the quantities in the data table are in a proportional relationship, we need to compare the ratios of the miles traveled to the hours biked. In a proportional relationship, the ratios between the two quantities should be constant.
To find the ratios, we divide the miles traveled by the hours biked:
For the first data point: 12 miles / 1 hour = 12
For the second data point: 26 miles / 2 hours = 13
For the third data point: 30 miles / 3 hours = 10
For the fourth data point: 48 miles / 4 hours = 12
Since the ratios are not the same for each data point, we can conclude that the quantities in the data table are not in a proportional relationship. Therefore, the correct answer is:
No, not all of the ratios are proportional or have equivalence.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of miles traveled to hours biked are consistent.
Let's calculate the ratios for each row:
- For the first row, the ratio is 12 miles / 1 hour = 12/1 = 12.
- For the second row, the ratio is 26 miles / 2 hours = 26/2 = 13.
- For the third row, the ratio is 30 miles / 3 hours = 30/3 = 10.
- For the fourth row, the ratio is 48 miles / 4 hours = 48/4 = 12.
Since the ratios are not consistent (12, 13, 10, 12), we can conclude that the quantities in the data table do not have a proportional relationship.
Therefore, the correct response is: No, not all of the ratios are proportional or have equivalence.