Question

related questions: lesson 5: inequalities

q. which inequality is represented in the graph shown below?

a. \\(y \ge -\frac{1}{2}x - 2\\)

b. \\(y > -\frac{1}{2}x - 2\\)

c. \\(y \le -\frac{1}{2}x - 2\\)

d. \\(y < -\frac{1}{2}x - 2\\)

Explanation:

Find the boundary line equation

Using the Solving Linear Inequalities knowledge point

$$
LATEXBLOCK0
$$

Determine the inequality symbol

The boundary line is dashed, which means the inequality is strict (\(>\) or \(<\)). The shaded region lies above the boundary line. Testing the point \((0,0)\):

$$ 0 > -\frac{1}{2}(0) - 2 \implies 0 > -2 \quad (\text{True}) $$

Thus, the inequality is:

$$ y > -\frac{1}{2}x - 2 $$

Answer:

• A. \(y \ge -\frac{1}{2}x - 2\)
• B. \(y > -\frac{1}{2}x - 2\) (Correct answer)
• C. \(y \le -\frac{1}{2}x - 2\)
• D. \(y < -\frac{1}{2}x - 2\)