Question

given the linear inequality graph, which statements are true? a point (-4, 2) is a solution. b the graph represents y > 3x - 6. c the graph represents y ≥ 3x - 6. d all points in the blue area are solutions. e points on the solid line are not solutions

Explanation:

• Option A: Point \((-4, 2)\) lies in the blue shaded area (solution region), so it is a solution.
• Option B: The line is solid (indicating \(\geq\) or \(\leq\)), not dashed (for \(>\) or \(<\)), so \(y > 3x - 6\) (dashed line) is incorrect.
• Option C: The solid line and shading above (or including the line) match \(y \geq 3x - 6\) (slope \(3\), y-intercept \(-6\)).
• Option D: By definition, the blue shaded area represents all solution points for the inequality.
• Option E: A solid line means points on the line are included (solutions), so this is false.

Answer:

A. Point \((-4, 2)\) is a solution,
C. The graph represents \(y \geq 3x - 6\),
D. All points in the blue area are solutions