which linear inequality is represented by the graph?\no y < 3x + 2\no y > 3x + 2\no y < 1/3x + 2\no y > 1/3x…

Answer:

A. $y<3x + 2$

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(-3,-7)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-7 - 2}{-3-0}=\frac{-9}{-3}=3$.

Step2: Determine the y - intercept

The line crosses the y - axis at the point $(0,2)$, so the y - intercept $b = 2$. The equation of the line is $y=3x + 2$.

Step3: Identify the inequality

The line is dashed, so the inequality is either $y>3x + 2$ or $y<3x + 2$. We test a point in the shaded region, say $(0,0)$. Substitute $x = 0$ and $y = 0$ into the inequalities. For $y<3x + 2$, we have $0<3\times0+2$ (i.e., $0 < 2$) which is true. For $y>3x + 2$, we have $0>3\times0+2$ (i.e., $0>2$) which is false. So the linear inequality is $y<3x + 2$.