Question

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

Using points (0,1) and (3,-1):
$$m=\frac{-1-1}{3-0}=-\frac{2}{3}$$

Step2: Identify line equation

Y-intercept is 1, so:
$$y=-\frac{2}{3}x+1$$

Step3: Determine inequality sign

Dashed line, shaded left (greater y):
$$y > -\frac{2}{3}x+1$$

Answer:

A. $y > -\frac{2}{3}x+1$