To determine which inequality corresponds to the blue region of the graph, we first need to understand the characteristics of the boundaries and the shading.
1. **Identifying the Boundary Line**:
- If the region is above the line represented by \( y = 3x - 1 \), then the inequality would be \( y > 3x - 1 \).
- If the region is below the line, it would be \( y < 3x - 1 \).
- If the region includes the line itself (solid line), it would involve \( \leq \) or \( \geq \).
- If the line is dotted (not included), it would involve \( < \) or \( > \).
2. **Analysis of Given Inequalities**:
- **\( y > 3x - 1 \)**
- **\( y < 1 - 3x \)**
- **\( x > 3y - 1 \)**
- **\( y \leq 3x - 1 \)**
Without the visual, I cannot definitively determine which inequality is correct. However, if the region is above the line with a solid boundary, the answer would be \( y \leq 3x - 1 \); if it is an open area above the line, then \( y > 3x - 1 \).
### Question 2: Which of the following ordered pairs is a solution to the inequality?
To check which of the given ordered pairs satisfies the inequalities accurately, we'll need to substitute into the proposed inequalities. Let's check the four pairs against both \( y > 3x - 1 \) and \( y \leq 3x - 1 \) for example:
1. **For \( (0, -3) \)**:
\[
-3 > 3(0) - 1 \quad \Rightarrow \quad -3 > -1 \quad \text{(False)}
\]
\[
-3 \leq 3(0) - 1 \quad \Rightarrow \quad -3 \leq -1 \quad \text{(False)}
\]
2. **For \( (3, 1) \)**:
\[
1 > 3(3) - 1 \quad \Rightarrow \quad 1 > 8 \quad \text{(False)}
\]
\[
1 \leq 3(3) - 1 \quad \Rightarrow \quad 1 \leq 8 \quad \text{(True)}
\]
3. **For \( (1, 2) \)**:
\[
2 > 3(1) - 1 \quad \Rightarrow \quad 2 > 2 \quad \text{(False)}
\]
\[
2 \leq 3(1) - 1 \quad \Rightarrow \quad 2 \leq 2 \quad \text{(True)}
\]
4. **For \( (0, 0) \)**:
\[
0 > 3(0) - 1 \quad \Rightarrow \quad 0 > -1 \quad \text{(True)}
\]
\[
0 \leq 3(0) - 1 \quad \Rightarrow \quad 0 \leq -1 \quad \text{(False)}
\]
### Conclusion for the Pairs:
- \( (3, 1) \) and \( (1, 2) \) are solutions if the inequality was \( y \leq 3x - 1 \).
- Depending on your graph (if it's above the line), only **(0, 0)** may be a solution if considering \( y > 3x - 1 \).
Choose based on the determined inequality from the graph and the points tested!