Question

graph the inequality.
$-24x + 8y \geq -48$
a)
b)

Explanation:

Step1: Isolate $y$ in the inequality

Start with the original inequality:
$$-24x + 8y \geq -48$$
Add $24x$ to both sides:
$$8y \geq 24x - 48$$

Step2: Simplify to slope-intercept form

Divide all terms by 8:
$$y \geq 3x - 6$$

Step3: Identify line and shading rules

• The boundary line is $y=3x-6$, which has a slope of 3 and y-intercept of -6. Since the inequality is $\geq$, the boundary line is solid (not dashed).
• The inequality $y \geq 3x-6$ means we shade the region above the boundary line.

(Note: Option A has a dashed line, which is incorrect for $\geq$. The correct graph will have a solid line $y=3x-6$ with shading above it, which matches the pattern of Option B's structure, even though the full graph is cut off.)

Answer:

B) [Graph with solid line $y=3x-6$ and shading above the line]