Question

Question

Use the table to answer the 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 non-proportional; the graph would be an arc.
The relationship is non-proportional; the graph would be an arc.

The proportional relationship cannot be determined from the information provided.
The proportional relationship cannot be determined from the information provided.

The relationship is proportional.

Answer 1

To determine if the relationship between time walking (minutes) and calories burned is proportional, we check if the ratio of calories burned to time walking is constant for each pair of values provided in the table.

Let's calculate the ratios for each time and calorie pair:

1. For 20 minutes: \( \frac{100 \text{ calories}}{20 \text{ minutes}} = 5 \)
2. For 30 minutes: \( \frac{150 \text{ calories}}{30 \text{ minutes}} = 5 \)
3. For 40 minutes: \( \frac{200 \text{ calories}}{40 \text{ minutes}} = 5 \)
4. For 60 minutes: \( \frac{300 \text{ calories}}{60 \text{ minutes}} = 5 \)
5. For 80 minutes: \( \frac{400 \text{ calories}}{80 \text{ minutes}} = 5 \)

Since the ratio of calories burned to time walking is constant (equal to 5) for all the given pairs, the relationship is proportional.

Correct Response: The relationship is proportional.