find the inequality represented by the graph.

Explanation:

Step1: Find the slope of the line

The line passes through points $(0, - 2)$ and $(1,2)$. The slope $m$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{2-(-2)}{1 - 0}=\frac{4}{1}=4$.

Step2: Find the y - intercept

The line crosses the y - axis at the point $(0,-2)$, so the y - intercept $b=-2$.

Step3: Write the equation of the line

The equation of a line in slope - intercept form is $y = mx + b$. Substituting $m = 4$ and $b=-2$, we get $y=4x - 2$.

Step4: Determine the inequality

The line is dashed, so the inequality is either $y>4x - 2$ or $y<4x - 2$. We can test a point in the shaded region, say $(0,0)$. Substituting $x = 0$ and $y = 0$ into $y-4x + 2$, we get $0-4\times0 + 2=2>0$. So the inequality is $y>4x - 2$.

Answer:

$y>4x - 2$