enter the correct answer in the box. write your answer in the form y = mx + b, using the appropriate…

enter the correct answer in the box. write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign. what inequality is shown in the graph?

enter the correct answer in the box. write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign. what inequality is shown in the graph?

Answer

Explanation:

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

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

Step2: Determine the inequality symbol

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

Answer:

$y>2x + 2$