which linear inequality is represented by the graph?\n$y > 2x + 3$\n$y < 2x + 3$\n$y > -2x + 3$\n$y < -2x + 3$

Explanation:

Step1: Find the slope - intercept form of the boundary line

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The y - intercept of the boundary line is $b = 3$ (the point where the line crosses the y - axis). To find the slope, we use two points on the line. Let's take $(0,3)$ and $(1,1)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1 - 3}{1-0}=- 2$. So the equation of the boundary line is $y=-2x + 3$.

Step2: Determine the inequality sign

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

Answer:

$y < -2x + 3$