Graphs of Proportional Relationships Quick Check

Question

5 of 55 of 5 Items

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 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 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.

Answer 1

To determine if the relationship between time walking (in minutes) and calories burned is proportional, we can check if the ratios of calories burned to time spent walking are constant.

Let's calculate the ratio of calories burned to time for each entry in the table:

• 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 time spent walking is constant (5 in each case), this indicates a proportional relationship.

Now, checking if the graph passes through the origin (0,0):

1. When no time is spent walking (0 minutes), logically, no calories are burned (0 calories).

Because the table indicates a constant ratio and passes through the origin, the correct response is:

The relationship is proportional.