Use the table to answer the question.

Question

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.

(1 point)
Responses

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 proportional relationship cannot be determined from the information provided.

The relationship is non-proportional; the graph would be an arc.

Answer 1

To determine if the relationship between time walking (in minutes) and calories burned is proportional, we need to check if the ratio of calories burned to time walked is constant for all the data points.

Let's calculate the ratio of calories burned to minutes walked for each time interval:

• For 20 minutes: \( \frac{100 \text{ calories}}{20 \text{ minutes}} = 5 \)
• For 30 minutes: \( \frac{150 \text{ calories}}{30 \text{ minutes}} = 5 \)
• For 40 minutes: \( \frac{200 \text{ calories}}{40 \text{ minutes}} = 5 \)
• For 60 minutes: \( \frac{300 \text{ calories}}{60 \text{ minutes}} = 5 \)
• For 80 minutes: \( \frac{400 \text{ calories}}{80 \text{ minutes}} = 5 \)

Since the ratio of calories burned to minutes walked is constant (5) for all the data points, the relationship is indeed proportional.

Thus, the correct response is:

The relationship is proportional.