Question

choose the correct inequality for this graph.
y ≥ (1/3)x - 1
y < 3x + 1
y ≤ 3x + 1
y > (1/3)x - 1

Explanation:

Step1: Find line equation

Use points $(3,0)$ and $(0,-1)$. Slope $m=\frac{0-(-1)}{3-0}=\frac{1}{3}$. Y-intercept $b=-1$. Equation: $y=\frac{1}{3}x-1$.

Step2: Identify line type

Line is dashed, so inequality uses $<$ or $>$.

Step3: Test shaded region

Test point $(0,0)$: $\frac{1}{3}(0)-1=-1$. $0 > -1$, so region is $y > \frac{1}{3}x - 1$.

Answer:

$y > \frac{1}{3}x - 1$