Time walking (minutes) 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.
Options:
The proportional relationship cannot be determined from the information provided
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 proportional
The relationship is non-proportional; the graph does not pass through the origin
To determine if the relationship is proportional, we need to check if there is a constant ratio between the time spent walking and the number of calories burned.
Let's calculate the ratio for each set of values:
- For the first set: 100/20 = 5
- For the second set: 150/30 = 5
- For the third set: 200/40 = 5
- For the fourth set: 300/60 = 5
- For the fifth set: 400/80 = 5
As we can see, the ratio of calories burned to time walking is always 5. This constant ratio indicates that the relationship between the time spent walking and the number of calories burned is proportional.
Therefore, the correct option is: The relationship is proportional.
To determine if the relationship is proportional, we need to check if the ratio of calories burned to time walking is the same for all values.
We can calculate the ratio for each pair of values:
- For 20 minutes of walking, the ratio is 100/20 = 5.
- For 30 minutes of walking, the ratio is 150/30 = 5.
- For 40 minutes of walking, the ratio is 200/40 = 5.
- For 60 minutes of walking, the ratio is 300/60 = 5.
- For 80 minutes of walking, the ratio is 400/80 = 5.
Since the ratio is the same (5) for all values, the relationship is proportional.
Therefore, the correct option is:
The relationship is proportional.