Hours Biked 1 2 3 4 Miles Traveled 12 26 30 48

Question

Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship, indicate why.

Answer 1

To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio between the hours biked and the miles traveled is the same for each pair of values.

Let's calculate the ratio for each pair:

For the first pair:
Hours Biked: 1
Miles Traveled: 12

Ratio: 12/1 = 12

For the second pair:
Hours Biked: 2
Miles Traveled: 26

Ratio: 26/2 = 13

For the third pair:
Hours Biked: 3
Miles Traveled: 30

Ratio: 30/3 = 10

For the fourth pair:
Hours Biked: 4
Miles Traveled: 48

Ratio: 48/4 = 12

As we can see, the ratios are not the same for each pair. Therefore, the quantities in the data table do not have a proportional relationship.