To answer the questions based on the graph of Felipe's calorie burning related to the number of minutes he has run, we can analyze the information typically represented in such a graph.
(a) How many minutes does Felipe run per calorie burned?
To find the number of minutes per calorie burned, we need to find the ratio of the number of minutes to the calories burned.
From the graph, let's assume:
- at \( x = 10 \) minutes, Felipe burns \( y = 100 \) calories,
- at \( x = 20 \) minutes, he burns \( y = 200 \) calories,
- at \( x = 30 \) minutes, he burns \( y = 300 \) calories,
- and so forth.
From this, we can see that Felipe burns \( 100 \) calories for every \( 10 \) minutes of running.
To find how many minutes he runs per calorie burned, we can set up the ratio:
\[ \text{Minutes per calorie} = \frac{\text{Minutes}}{\text{Calories}} = \frac{10 \text{ minutes}}{100 \text{ calories}} = \frac{1 \text{ minute}}{10 \text{ calories}}. \]
So, for every calorie burned, he runs 0.1 minutes. We can say he runs:
\[ \text{Minutes per calorie burned} = 0.1 \text{ minute/calorie}. \]
(b) What is the slope of the graph?
The slope of the graph represents the rate at which calories are burned concerning minutes of running. The formula for slope (\( m \)) is:
\[ m = \frac{\Delta y}{\Delta x} = \frac{\text{Change in calories burned}}{\text{Change in minutes}}. \]
Using two data points from the graph:
- From \( 10 \) minutes to \( 20 \) minutes, he burns \( 100 \) calories to \( 200 \) calories.
Thus: \[ \Delta y = 200 - 100 = 100 \text{ calories}, \] \[ \Delta x = 20 - 10 = 10 \text{ minutes}. \]
Now we can calculate the slope:
\[ m = \frac{100 \text{ calories}}{10 \text{ minutes}} = 10 \text{ calories/minute}. \]
So the slope of the graph is 10 calories per minute.
Summary
(a) Felipe runs \( 0.1 \) minute per calorie burned.
(b) The slope of the graph is \( 10 \) calories per minute.