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The equation provided is \( x + 3y = 6 \), and the task is to select all coordinate pairs that represent a solution to this equation.

To verify which points are valid, we substitute the values from each coordinate pair into the equation \( x + 3y = 6 \) and check if the equation holds true.

Let's test each pair:

- **A. (0, 2):**
  \[
  x + 3y = 0 + 3(2) = 0 + 6 = 6 \quad (\text{True})
  \]
  **A** is a solution.

- **B. (0, 6):**
  \[
  x + 3y = 0 + 3(6) = 0 + 18 = 18 \quad (\text{False})
  \]
  **B** is not a solution.

- **C. (2, 6):**
  \[
  x + 3y = 2 + 3(6) = 2 + 18 = 20 \quad (\text{False})
  \]
  **C** is not a solution.

- **D. (3, 1):**
  \[
  x + 3y = 3 + 3(1) = 3 + 3 = 6 \quad (\text{True})
  \]
  **D** is a solution.

- **E. (4, 1):**
  \[
  x + 3y = 4 + 3(1) = 4 + 3 = 7 \quad (\text{False})
  \]
  **E** is not a solution.

- **F. (6, 2):**
  \[
  x + 3y = 6 + 3(2) = 6 + 6 = 12 \quad (\text{False})
  \]
  **F** is not a solution.

### Correct answers: A and D

Let me know if you would like further clarification or details.

Here are 5 related questions to expand your understanding:
1. What is the slope-intercept form of the equation \(x + 3y = 6\)?
2. How would you graph \(x + 3y = 6\) using intercepts?
3. How can you verify if a point lies on the graph of a linear equation?
4. What are the x-intercept and y-intercept of the equation \(x + 3y = 6\)?
5. How does changing the constant in the equation \(x + 3y = 6\) affect the graph?

**Tip**: Always substitute the coordinates into the equation to verify if a point is a solution to the given equation.

Select all coordinate pairs that represent a solution to the equation x + 3y = 6.

Learn how to solve the linear equation x + 3y = 6 by identifying correct coordinate pairs. This problem focuses on key algebraic concepts and is suitable for students in Grades 7-9.

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