To address Felipe's running and the calories burned, let's analyze the given information step by step.
Part (a): How many minutes does Felipe run per calorie burned?
From the graph, it appears that the relationship between calories burned (y-axis) and the number of minutes run (x-axis) is linear, with a direct variation between the two.
If we know the points on the graph:
- For example, at 10 minutes, if he has burned 100 calories, then we can calculate the ratio of minutes to calories burned.
To find how many minutes he runs per calorie burned, we can take two data points:
- At 10 minutes, 100 calories burned.
- At 40 minutes, 400 calories burned.
Using the first point:
- At 10 minutes, 100 calories → \( \frac{10 \text{ minutes}}{100 \text{ calories}} \) = 0.1 minute per calorie.
Thus, Felipe runs 0.1 minute per calorie burned.
Part (b): What is the slope of the graph?
The slope of a graph that shows a direct variation can be found using the formula for the slope, which is:
\[ \text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{\Delta y}{\Delta x} \]
Using our previous points:
- From (10 minutes, 100 calories) to (40 minutes, 400 calories), we can compute the change:
- \(\Delta y = 400 - 100 = 300\) calories
- \(\Delta x = 40 - 10 = 30\) minutes
So now we can calculate the slope:
\[ \text{slope} = \frac{300 \text{ calories}}{30 \text{ minutes}} = 10 \text{ calories per minute} \]
Thus, the slope of the graph is 10 calories per minute.
Summary:
(a) 0.1 minute(s) per calorie burned. (b) The slope of the graph is 10 calories per minute.