Question

graph the inequality on a plane. (click to shade a region below or above the line).
$y < -2x - 2$
toggle lines solidity

Explanation:

Step1: Identify line type

The inequality is $y < -2x - 2$, which uses a strict less-than sign ($<$), so the boundary line $y=-2x-2$ must be dashed (not solid) to show points on the line are not included.

Step2: Determine shading region

Test a point not on the line, e.g., $(0,0)$:
Substitute into inequality: $0 < -2(0) - 2$ → $0 < -2$, which is false.
Since the test point above the line fails, shade the region below the dashed line.

Step3: Verify line intercepts

For $y=-2x-2$:

• y-intercept: when $x=0$, $y=-2$
• x-intercept: when $y=0$, $0=-2x-2$ → $x=-1$

These match the plotted line's intercepts, so adjust the line to be dashed, then shade below it.

Answer:

1. First, set the boundary line $y=-2x-2$ to be dashed (use the "Toggle Line's Solidity" button to change from solid to dashed).
2. Shade the entire region below this dashed line.