Question

identifying an inequality from its graph
which inequality is represented by the graph?
$\circ$ $y > \frac{2}{3}x + 1$
$\circ$ $y < \frac{2}{3}x + 1$
$\circ$ $y < -\frac{3}{2}x + 1$
$\circ$ $y > -\frac{3}{2}x + 1$

Explanation:

Step1: Find line slope & intercept

The line passes through $(0,1)$ and $(3,-1)$. Slope $m=\frac{-1-1}{3-0}=-\frac{2}{3}$, y-intercept $b=1$. Line equation: $y=-\frac{2}{3}x+1$.

Step2: Analyze line style & shading

Dashed line means $<$ or $>$. Shading is below the line, so use $<$.

Step3: Match to options

The inequality is $y < -\frac{2}{3}x+1$.

Answer:

$y < -\frac{2}{3}x+1$ (third option)