which linear inequality is represented by the graph?\n$yleq2x + 4$\n$yleq\frac{1}{2}x+3$\n$ygeq\frac{1}{2}x…

Explanation:

Step1: Find the slope and y - intercept of the line

The line passes through the points (-2,2) and (0,3). The slope $m$ is calculated as $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 2}{0-(-2)}=\frac{1}{2}$. The y - intercept $b$ is the y - value when $x = 0$, so $b = 3$. 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 $\geq$. We test a point in the shaded region, say $(0,0)$. Substitute $x = 0$ and $y = 0$ into the inequalities. For $y\leq\frac{1}{2}x+3$, we have $0\leq\frac{1}{2}(0)+3$, which is $0\leq3$ (true). For $y\geq\frac{1}{2}x + 3$, we have $0\geq\frac{1}{2}(0)+3$, which is $0\geq3$ (false).

Answer:

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