time 20 30 40 60 80
calories burned 100 150 200 300 400 the table shows a relationship between the amount of time spent walking and the number of calories burned. Determine if the relationship is proportional. (1 point) Responses The relationship is non-proportional; the graph would be an arc. The relationship is non-proportional; the graph would be an arc. The relationship is non-proportional; the graph does not pass through the origin. The relationship is non-proportional; the graph does not pass through the origin. The relationship is proportional. The relationship is proportional. The proportional relationship cannot be determined from the information provided.
The relationship is non-proportional; the graph does not pass through the origin.
To determine if the relationship between the amount of time spent walking and the number of calories burned is proportional, we need to check if the ratio of time to calories remains constant.
Let's calculate the ratio for each data point:
20 minutes: 100 calories -> ratio = 20/100 = 0.2
30 minutes: 150 calories -> ratio = 30/150 = 0.2
40 minutes: 200 calories -> ratio = 40/200 = 0.2
60 minutes: 300 calories -> ratio = 60/300 = 0.2
80 minutes: 400 calories -> ratio = 80/400 = 0.2
Since the ratio is the same for all data points (0.2), we can conclude that the relationship is proportional.
To determine if the relationship between the amount of time spent walking and the number of calories burned is proportional, we need to check if the ratio of calories burned to time is constant.
Let's calculate the ratios:
For 20 minutes: 100 calories / 20 minutes = 5 calories per minute
For 30 minutes: 150 calories / 30 minutes = 5 calories per minute
For 40 minutes: 200 calories / 40 minutes = 5 calories per minute
For 60 minutes: 300 calories / 60 minutes = 5 calories per minute
For 80 minutes: 400 calories / 80 minutes = 5 calories per minute
Since the ratio of calories burned to time is constant at 5 calories per minute for all data points, we can conclude that the relationship is proportional.
Therefore, the correct response is: The relationship is proportional.