Question

which linear inequality is represented by the graph? $\circ$ $y\leq \frac{1}{3}x - 1$ $\circ$ $y\geq \frac{1}{3}x - 1$ $\circ$ $y < 3x - 1$ $\circ$ $y > 3x - 1$

Explanation:

Step1: Find line slope & intercept

Using points $(3,0)$ and $(0,-1)$:
Slope $m=\frac{0-(-1)}{3-0}=\frac{1}{3}$, y-intercept $b=-1$.
Line equation: $y=\frac{1}{3}x-1$

Step2: Check line style & shading

Solid line means $\leq$ or $\geq$. Shading above line means $y\geq$ the line.

Answer:

$\boldsymbol{y \geq \frac{1}{3}x - 1}$ (Option B)