To determine the number of calories Christine is burning per minute and the slope of the graph, we can analyze the relationship represented by the graph.
(a) How many calories is Christine burning per minute?
From the graph, let's identify two points that it passes through. Assuming we have the following points:
- Point 1: (10 minutes, 50 calories)
- Point 2: (30 minutes, 100 calories)
To find out how many calories Christine is burning per minute, we need to find the change in calories over the change in minutes.
Using the points we identified:
- Change in calories = \(100 \text{ calories} - 50 \text{ calories} = 50 \text{ calories}\)
- Change in time = \(30 \text{ minutes} - 10 \text{ minutes} = 20 \text{ minutes}\)
Now, use these changes to find the rate of calories burned per minute:
\[ \text{Calories burned per minute} = \frac{\text{Change in calories}}{\text{Change in time}} = \frac{50 \text{ calories}}{20 \text{ minutes}} = 2.5 \text{ calories per minute} \]
So, Christine is burning 2.5 calories per minute.
(b) What is the slope of the graph?
The slope of the graph is the same as the rate of change we calculated in part (a).
Using the same calculation, we have:
\[ \text{slope} = \frac{\text{Change in calories}}{\text{Change in minutes}} = \frac{50 \text{ calories}}{20 \text{ minutes}} = 2.5 \]
Therefore, the slope of the graph is also 2.5.