Question

Question was provided via image upload.

Explanation:

Identify the boundary line equation

The boundary line is dashed and passes through the points \((0, -2)\) and \((-3, 0)\).

$$ \text{Slope } m = \frac{0 - (-2)}{-3 - 0} = -\frac{2}{3} $$

$$ \text{Equation of the line: } y = -\frac{2}{3}x - 2 $$

Determine the inequality sign

The shaded region is below the dashed boundary line.

$$ y < -\frac{2}{3}x - 2 $$

Match with the correct graph option

• Option 1 (top): Shaded region is above the dashed line \(y > -\frac{2}{3}x - 2\).
• Option 2 (middle): Shaded region is below the dashed line \(y < -\frac{2}{3}x - 2\).
• Option 3 (bottom): Shaded region is below a solid line \(y \le -\frac{2}{3}x - 2\).

Answer:

• (A) Shaded region above the dashed line
• (B) Shaded region below the dashed line (Correct answer)
• (C) Shaded region below the solid line