https://file.aiquickdraw.com/mathbot/file/1728326998650ek0mvobn.jpg

Let's analyze the graph and solve the given questions.

The graph represents a direct variation between the number of minutes Deandre has studied and the number of calories he has burned. It seems to show a linear relationship.

To solve the questions:

### (a) How many calories is Deandre burning per minute?
We need to find the rate of change, which is the slope of the line. The slope is defined as:

\[
\text{slope} = \frac{\text{change in y (minutes)}}{\text{change in x (calories burned)}}
\]

From the graph, we can pick two points to calculate the slope. Let's select two points:
- Point 1: (0, 0) (where both calories burned and minutes studied are 0)
- Point 2: (200, 80) (where Deandre burned 200 calories and studied for 80 minutes)

Now, apply the slope formula:

\[
\text{slope} = \frac{80 - 0}{200 - 0} = \frac{80}{200} = 0.4
\]

Thus, Deandre burns **0.4 calories per minute**.

### (b) What is the slope of the graph?
The slope of the graph is **0.4**. This is the same as the answer for (a) since the slope represents the rate at which Deandre burns calories per minute.

### Summary:
- (a) **0.4 calories per minute**
- (b) **0.4**

Would you like more details or clarifications on the solution?

Here are five follow-up questions to expand the discussion:
1. What does it mean when a graph shows a direct variation?
2. How would the graph look if Deandre burned calories at a slower rate?
3. What would happen to the slope if Deandre studied for the same amount of time but burned more calories?
4. Can you explain the relationship between slope and unit rates?
5. How would you calculate the number of calories burned if Deandre studied for 120 minutes?

**Tip**: In a linear graph, the slope can always be interpreted as the rate of change between the two variables being graphed.

How many calories is Deandre burning per minute? What is the slope of the graph?

Learn how to calculate the rate at which Deandre burns calories while studying, using the graph of his study time and calories burned. Understand the concept of slope and direct variation in a step-by-step solution. Suitable for students in Grades 6-8.

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