Question

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

Explanation:

Step1: Identify blue line equation

The blue line has y-intercept $b=2$, slope $m=-2$. Using $y=mx+b$, we get $y=-2x+2$.

Step2: Check line type and shading

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

Step3: Match with options

The inequality is $y < -2x + 2$, which matches the second option.

Answer:

$y < -2x + 2$