which linear inequality is represented by the graph?\no $y<\\frac{2}{3}x + 3$\no $y>\\frac{3}{2}x + 3$\no…

which linear inequality is represented by the graph?\no $y<\\frac{2}{3}x + 3$\no $y>\\frac{3}{2}x + 3$\no $y>\\frac{2}{3}x + 3$\no $y<\\frac{3}{2}x + 3$

which linear inequality is represented by the graph?\no $y<\\frac{2}{3}x + 3$\no $y>\\frac{3}{2}x + 3$\no $y>\\frac{2}{3}x + 3$\no $y<\\frac{3}{2}x + 3$

Answer

Answer:

C. $y>\frac{2}{3}x + 3$

Explanation:

Step1: Find the slope and y - intercept

The line equation is $y=mx + b$, where $m$ is slope and $b$ is y - intercept. The line crosses y - axis at $y = 3$, so $b = 3$. Using two points on the line $(0,3)$ and $(3,5)$, slope $m=\frac{5 - 3}{3-0}=\frac{2}{3}$. So the line equation is $y=\frac{2}{3}x+3$.

Step2: Determine the inequality sign

The line is dashed, so the inequality is either $y>\frac{2}{3}x + 3$ or $y<\frac{2}{3}x + 3$. The shaded region is above the line, so the inequality is $y>\frac{2}{3}x + 3$.