Question

which linear inequality is represented by the graph?
\\( y < \frac{2}{3}x + 3 \\)
\\( y > \frac{3}{2}x + 3 \\)
\\( y > \frac{2}{3}x + 3 \\)
\\( y < \frac{3}{2}x + 3 \\)

Explanation:

Step1: Find slope of boundary line

The line passes through $(0,3)$ and $(3,5)$. Slope $m=\frac{5-3}{3-0}=\frac{2}{3}$.

Step2: Identify y-intercept

The line crosses y-axis at $(0,3)$, so $b=3$. Equation: $y=\frac{2}{3}x+3$.

Step3: Determine inequality sign

Boundary is dashed, shaded area is above the line, so use $>$.

Answer:

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