which linear inequality is represented by the graph?\n$y>\frac{2}{3}x - \frac{1}{5}$\n$ygeq\frac{3}{2}x+\frac…

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)=(0,0.2)$ and $(x_2,y_2)=(3,2.2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2.2 - 0.2}{3-0}=\frac{2}{3}$.

Step2: Find the y - intercept

The y - intercept $b$ is the y - value when $x = 0$. From the point $(0,0.2)$, $b = 0.2=\frac{1}{5}$.

Step3: Determine the inequality

The line is solid, so the inequality is either $\leq$ or $\geq$. The shaded region is below the line, so the inequality is $y\leq$. The equation of the line is $y=\frac{2}{3}x+\frac{1}{5}$, so the linear inequality is $y\leq\frac{2}{3}x+\frac{1}{5}$.

Answer:

$y\leq\frac{2}{3}x+\frac{1}{5}$