this is the graph of a linear inequality. write the inequality in slope - intercept form. write your answer…

this is the graph of a linear inequality. write the inequality in slope - intercept form. write your answer with y first, followed by an inequality symbol. use integers, proper fractions, and improper fractions in simplest form.

this is the graph of a linear inequality. write the inequality in slope - intercept form. write your answer with y first, followed by an inequality symbol. use integers, proper fractions, and improper fractions in simplest form.

Answer

Explanation:

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

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

Step2: Determine the inequality symbol

The line is dashed, so the inequality is either $y<-x + 2$ or $y>-x + 2$. We test a point in the shaded region, say $(0,3)$. Substitute $x = 0$ and $y = 3$ into the inequalities. For $y<-x + 2$, we have $3<0 + 2$ (false). For $y>-x + 2$, we have $3>0+2$ (true).

Answer:

$y>-x + 2$