Question

which linear inequality is represented by the graph?
○ $y < 3x + 2$
○ $y > 3x + 2$
○ $y < \frac{1}{3}x + 2$
○ $y > \frac{1}{3}x + 2$

Explanation:

Step1: Find the line's slope

Use points $(0,2)$ and $(-3,-7)$:
$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-2}{-3-0}=\frac{-9}{-3}=3$$

Step2: Find line equation

Y-intercept $b=2$, so:
$$y=3x+2$$

Step3: Determine inequality sign

Shaded region is below the solid line:
$$y \leq 3x+2$$
Match to options (solid line includes equality, $y<3x+2$ aligns with shaded area below the line).

Answer:

y < 3x + 2