Proportional Relationships in Tables Quick Check
4 of 54 of 5 Items
Question
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, you can’t bike 12 miles in an hour.
No, you can’t bike 12 miles in an hour.
No, none of the ratios have equivalence.
No, none of the ratios have equivalence.
No, not all of the ratios are proportional or have equivalence.
No, not all of the ratios are proportional or have equivalence.
Yes, this data table has a proportional relationship.
Yes, this data table has a proportional relationship.
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 between the hours biked and miles traveled are equivalent. Let's calculate the ratios:
Ratio for 1 hour: 12 miles / 1 hour = 12
Ratio for 2 hours: 26 miles / 2 hours = 13
Ratio for 3 hours: 30 miles / 3 hours = 10
Ratio for 4 hours: 48 miles / 4 hours = 12
As we can see, the ratios are not all equivalent. For example, the ratio for 2 hours is not equal to the ratio for 1 hour. Therefore, the quantities in the data table do not have a proportional relationship.
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 can check if the ratios of miles traveled to hours biked are equal for all rows.
Let's calculate these ratios:
For the first row, the ratio of miles traveled to hours biked is 12/1 = 12.
For the second row, the ratio of miles traveled to hours biked is 26/2 = 13.
For the third row, the ratio of miles traveled to hours biked is 30/3 = 10.
For the fourth row, the ratio of miles traveled to hours biked is 48/4 = 12.
Since the ratios are not equal for all rows, 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.