https://file.aiquickdraw.com/mathbot/file/1727362270352gwx9d8gx.jpg

The problem on the image is asking for a direct variation equation that describes the relationship between the number of calories and the grams of protein.

### Problem 6:
- The number of calories **varies directly** with the number of grams of protein. We are tasked with writing a direct variation equation and then using that equation to determine the number of calories from **25 grams of protein**.

#### General form of direct variation:
The direct variation equation can be written as:
\[
C = kP
\]
Where:
- \(C\) is the number of calories,
- \(P\) is the grams of protein,
- \(k\) is the constant of variation.

#### From the graph (left side of the image):
We can determine the constant \(k\) using the data points. The graph shows that for 10 grams of protein, the calories are 50. Thus, we can use the point \( (P = 10, C = 50) \) to find \(k\):
\[
50 = k \cdot 10 \implies k = \frac{50}{10} = 5
\]

Thus, the direct variation equation is:
\[
C = 5P
\]

#### Finding the calories for 25 grams of protein:
Now, use this equation to determine the calories for 25 grams of protein:
\[
C = 5 \cdot 25 = 125
\]

So, there are **125 calories** in 25 grams of protein.

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Do you want further details on this? 

Here are five related questions you could explore:
1. How do you identify direct variation from a graph?
2. What happens when the constant of variation is negative?
3. Can you solve for the grams of protein given a certain number of calories?
4. How does this concept apply to other real-world examples like distance and time?
5. What is the relationship between direct variation and linear equations?

**Tip**: When working with direct variation, always check if the ratio between the variables is constant across different data points.

The number of calories varies directly with the number of grams of protein. Write a direct variation equation that describes the relationship. Use your equation to determine the number of calories from 25 grams of protein.

Learn how to solve a direct variation problem involving the relationship between calories and grams of protein. The solution includes identifying the constant of variation from a graph and calculating the number of calories in 25 grams of protein. Suitable for Grades 7-9.

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