which linear inequality is represented by the graph?\no y>2x + 3\no y<2x + 3\no y>-2x + 3\no y<-2x + 3

Explanation:

Step1: Find the slope - intercept form of the 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 line in the graph is $b = 3$. The line passes through the points $(0,3)$ 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 line is $y=-2x + 3$.

Step2: Determine the inequality

The line is dashed, so the inequality is either $y>-2x + 3$ or $y<-2x + 3$. We can test a point in the shaded region. Let's test the point $(0,0)$. Substitute $x = 0$ and $y = 0$ into the inequalities. For $y>-2x + 3$, we have $0>-2\times0+3$ or $0 > 3$ (false). For $y<-2x + 3$, we have $0<-2\times0+3$ or $0 < 3$ (true).

Answer:

$y < - 2x+3$