Question

identifying an inequality from its graph
analyze the graph. which inequality represents the graph?
○ $y > -\frac{1}{3}x + 4$
○ $y < -\frac{1}{3}x + 4$
○ $y > -3x + 4$
○ $y < -3x + 4$

Explanation:

Step1: Find line slope & intercept

The line passes through $(0,4)$ and $(1,1)$. Slope $m=\frac{1-4}{1-0}=-3$, y-intercept $b=4$. Line equation: $y=-3x+4$.

Step2: Determine inequality symbol

The line is dashed, so use $<$ or $>$. The shaded region is below the line, so use $<$.

Answer:

$y < -3x + 4$ (the fourth option)