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

1 answer

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.