Question

in which of the following does the shaded region represent the solution set to $y \leq -\frac{2}{3}x - 1$?
choose 1 answer:
a
graph a
b
graph b
c
graph c
d
graph d

Explanation:

Step1: Identify line slope & intercept

The inequality is $y \leq -\frac{2}{3}x - 1$. The corresponding line has slope $m=-\frac{2}{3}$ (negative, so line falls left to right) and y-intercept $b=-1$ (crosses y-axis at $(0,-1)$).

Step2: Determine shading direction

Since the inequality is $y \leq$ [line equation], we shade below the line.

Step3: Match to options

• Option A: Line has positive slope (rises left to right) → incorrect.
• Option B: Line has negative slope, y-intercept ~-1, shaded below → correct.
• Option C: Line has positive slope, shaded above → incorrect.
• Option D: Line has negative slope, shaded above → incorrect.

Answer:

B. (The graph with a downward-sloping line crossing the y-axis below the origin, with the region below the line shaded)