Question

which inequality pairs with ( y leq -2x - 1 ) to complete the system of linear inequalities represented by the graph?
( \bigcirc ) ( y < -2x + 2 )
( \bigcirc ) ( y > -2x + 2 )
( \bigcirc ) ( y < 2x - 2 )
( \bigcirc ) ( y > 2x - 2 )

Explanation:

Step1: Identify second line's equation

First, find the slope-intercept form ($y=mx+b$) of the dashed line. The line passes through $(0,2)$ and $(1,0)$.
Slope $m=\frac{0-2}{1-0}=-2$, y-intercept $b=2$. So equation is $y=-2x+2$.

Step2: Determine inequality direction

The shaded region for this line is above the dashed line, and dashed line means no equality, so use $>$.

Answer:

$y>-2x+2$ (Option B)