Question

Question was provided via image upload.

Explanation:

Identify the boundary line equation

The boundary line is solid and passes through the points \((-5, 0)\) and \((0, -2)\).

$$ m = \frac{-2 - 0}{0 - (-5)} = -\frac{2}{5} $$

$$ y = -\frac{2}{5}x - 2 \implies 2x + 5y = -10 $$

Determine the inequality sign

The shaded region in the top graph contains the origin \((0,0)\).

$$ 2(0) + 5(0) = 0 \ge -10 $$

Thus, the top graph represents the inequality:

$$ 2x + 5y \ge -10 \implies y \ge -\frac{2}{5}x - 2 $$

Match with the correct option

The top option is selected, representing the region containing the origin:

$$ y \ge -\frac{2}{5}x - 2 $$

Answer:

• (A) Shaded region above the solid line \(y = -\frac{2}{5}x - 2\) (including the origin) (Correct answer)
• (B) Shaded region below the solid line \(y = -\frac{2}{5}x - 2\) (excluding the origin)