write an inequality represented by the graph.

Explanation:

Step1: Find the slope - intercept form of the line

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

Step2: Determine the inequality

Since the line is dashed, the inequality is either $y<-x - 2$ or $y>-x - 2$. We can test a point in the shaded region, say $(0,0)$. Substituting $x = 0$ and $y = 0$ into $y<-x - 2$ gives $0<-0 - 2$ (false), and substituting into $y>-x - 2$ gives $0>-0 - 2$ (true).

Answer:

$y>-x - 2$