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

Explanation:

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

The line passes through the points (-4,0) and (0,2). The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{2 - 0}{0-(-4)}=\frac{2}{4}=\frac{1}{2}$, and the y - intercept $b = 2$. The equation of the line is $y=\frac{1}{2}x + 2$.

Step2: Determine the inequality

The line is solid, so the inequality is either $y\leq\frac{1}{2}x + 2$ or $y\geq\frac{1}{2}x + 2$. We test a point in the shaded region, say $(0,0)$. Substitute $x = 0$ and $y = 0$ into the inequalities. For $y\leq\frac{1}{2}x+2$, we have $0\leq\frac{1}{2}(0)+2$, which is $0\leq2$ (true). For $y\geq\frac{1}{2}x + 2$, we have $0\geq\frac{1}{2}(0)+2$, which is $0\geq2$ (false).

Answer:

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