To determine how many calories Michael is burning per minute and the slope of the graph based on the information provided:
(a) Since the graph indicates that the number of calories burned (y) varies directly with the number of minutes walked (x), we can use any two points on the graph to determine the rate of calorie burn per minute.
Let's take two points from the graph to calculate the rate: For example:
- Point 1: (10 minutes, 40 calories)
- Point 2: (20 minutes, 80 calories)
To find the calories burned per minute, we can calculate the change in calories burned divided by the change in minutes walked.
\[ \text{Calories burned per minute} = \frac{\Delta y}{\Delta x} = \frac{80 - 40}{20 - 10} = \frac{40}{10} = 4 \text{ calories per minute} \]
Thus, Michael is burning 4 calories per minute.
(b) The slope of the graph is actually the same as the rate we calculated in part (a), since the slope of a line in a graph is defined as the change in the y-value divided by the change in the x-value.
Therefore, the slope of the graph is also 4.