Hours Biked 1 2 3 4 Miles Traveled 12 26 30 48
Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship, indicate why.
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.
To determine if the quantities in the data table are in a proportional relationship, we can check if the ratio of miles traveled to hours biked is constant.
If we calculate the ratios for each data point, we get:
Ratio for data point 1: 12/1 = 12
Ratio for data point 2: 26/2 = 13
Ratio for data point 3: 30/3 = 10
Ratio for data point 4: 48/4 = 12
Since the ratios are not equal for all data points, the quantities in the data table do not have a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if there is a constant ratio between the miles traveled and the hours biked.
To find the ratio, we divide the miles traveled by the hours biked for each data point:
For the first data point (1 hour biked, 12 miles traveled), the ratio is 12/1 = 12.
For the second data point (2 hours biked, 26 miles traveled), the ratio is 26/2 = 13.
For the third data point (3 hours biked, 30 miles traveled), the ratio is 30/3 = 10.
For the fourth data point (4 hours biked, 48 miles traveled), the ratio is 48/4 = 12.
Since the ratios are not the same for all data points, the quantities in the data table do not have a proportional relationship. The ratios are not constant, indicating that there is not a fixed ratio between the miles traveled and the hours biked.