https://file.aiquickdraw.com/mathbot/file/1726065630830ep1shiot.jpg

To solve the problem, let's break it down:

You are given the inequality \( x + y > 5 \) and asked to test the point \( (0, 0) \).

1. **Substitute the test point \( (0, 0) \) into the inequality**:
   \[
   x + y > 5 \quad \text{becomes} \quad 0 + 0 > 5
   \]
   \[
   0 > 5 \quad \text{(which is false)}.
   \]

Since the test point \( (0,0) \) does not satisfy the inequality (it proves false), you should shade the region opposite to where \( (0,0) \) is located relative to the line \( x + y = 5 \).

2. **Determine where the line \( x + y = 5 \) is located**:
   - This line is the boundary for the inequality \( x + y > 5 \). The points above this line (where the sum of \( x \) and \( y \) is greater than 5) satisfy the inequality.
   
   - The point \( (0, 0) \) is below the line \( x + y = 5 \), and since the test point makes the inequality false, you shade the opposite region — which is above the line.

So, the correct answer is **a. Above the line**.

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Would you like further details on graphing inequalities or the steps? Here are five related questions to deepen your understanding:

1. How do you find the slope and intercept of the line \( x + y = 5 \)?
2. What happens when the inequality sign is \( \geq \) instead of \( > \)?
3. How do you know when to use a dashed line versus a solid line when graphing an inequality?
4. Can you test other points to verify the shading region for this inequality?
5. How would you graph \( x + y < 5 \) instead?

**Tip**: Always use a test point not on the line (commonly \( (0,0) \) if it’s not on the boundary) to determine the shading region.

When using the test point (0,0) for the inequality x + y > 5, and it proves false, where should you shade?

Learn how to graph the linear inequality x + y > 5 by testing points and determining where to shade. This problem covers key concepts like linear inequalities, graphing, and shading regions. Suitable for Grades 9-11.

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