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To solve this problem, let's examine the given information:

1. The relationship between the amounts of red paint (\(y\)) and blue paint (\(x\)) is depicted in a graph.
2. We need to determine the ratio of red paint to blue paint.

### Step-by-Step Solution:
The graph shows a point labeled \((9, 27)\), where:
- \(x = 9\) (amount of blue paint in quarts)
- \(y = 27\) (amount of red paint in quarts)

The ratio of red paint to blue paint can be calculated as:
\[
\text{Ratio of red to blue} = \frac{y}{x} = \frac{27}{9} = 3 : 1
\]

Thus, the correct answer is:
- **3 : 1**

Would you like more details on the solution process, or do you have any questions?

Here are five related questions that might expand your understanding:
1. How would the ratio change if the point on the graph were \((10, 30)\)?
2. What is a direct proportion, and how does it relate to the graph shown?
3. How would you find the ratio if the graph point was not an integer?
4. If only the total paint is known, how can you determine individual quantities using the ratio?
5. How does changing the ratio affect the shade of purple produced?

**Tip:** Ratios are a way to express relationships between two quantities. Simplifying ratios helps to see the proportion more clearly.

A certain shade of purple paint is made by mixing blue and red paint. The relationship between the number of quarts of blue paint in the mix, x, and the number of quarts of red paint, y, is represented by the graph. What is the ratio of red paint to blue paint?

Solve the problem of finding the ratio of red paint to blue paint using a graph. The example uses quarts of blue and red paint, where the graph shows a point (9, 27). Learn how to calculate the ratio and understand the relationship between the variables. Suitable for Grades 6-8.

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