which linear inequality is represented by the graph?\no y≤2x + 4\no y≤1/2x + 3\no y≥1/2x + 3\no y≥2x + 3

Explanation:

Step1: Find the slope and y - intercept

The line passes through points (-2, 2) and (0, 3). The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 2}{0-(-2)}=\frac{1}{2}$. The y - intercept $b = 3$ (where the line crosses the y - axis). So the equation of the line is $y=\frac{1}{2}x + 3$.

Step2: Determine the inequality sign

The line is solid, so the inequality is either $\leq$ or $\geq$. The shaded region is below the line, so the inequality is $y\leq\frac{1}{2}x + 3$.

Answer:

$y\leq\frac{1}{2}x + 3$