Question

Select the inequality that is represented by the blue region of the graph.



(1 point)
Responses

y>3x−1
y is greater than 3 x minus 1

y<1−3x
y<1−3x

y≤3x−1
y is less than or equal to 3 x minus 1

x>3y−1

Answer 1

To determine which inequality corresponds to the blue region of the graph, we need to look at the characteristics of the line and the shading of the region.

1. **Identify the line**: First, if the boundary line is given by the equation \( y = 3x - 1 \), we use this line to consider possible inequalities.

2. **Determine if the line is included**: If the blue region includes the line itself, then the inequality will use \( \leq \) or \( \geq \). If it doesn't include the line, it will use \( < \) or \( > \).

3. **Check the direction of shading**:
- If the shading is above the line, it would correspond to \( y > 3x - 1 \) or \( y \geq 3x - 1 \).
- If the shading is below the line, it would correspond to \( y < 3x - 1 \) or \( y \leq 3x - 1 \).

4. **Choose the correct inequality**:
- If the line is \( y = 3x - 1 \) and the blue region is above this line (excluding the line), then we select \( y > 3x - 1 \).
- If the line is \( y = 3x - 1 \) and the blue region is below this line (including the line), then we select \( y \leq 3x - 1 \).
- If we have \( y = 1 - 3x \) and the blue region is above this line, we select \( y < 1 - 3x \).

Given this reasoning, if the information describes the blue region as being above the line where \( y = 3x - 1 \), the inequality **y > 3x - 1** would be the correct choice. If the blue region is below this line and includes it, the correct choice would be **y ≤ 3x−1**.

Without seeing the graph, I cannot definitively pick one, but the analysis follows these steps. Please check the graph to match the situation described above.