Question

graph the inequality.
$y \leq -2x - 4$

Explanation:

Step1: Identify boundary line

The inequality $y \leq -2x - 4$ has a boundary line $y = -2x - 4$. Since the inequality is $\leq$, the line will be solid.

Step2: Find intercepts of boundary

• x-intercept: Set $y=0$:

$0 = -2x - 4$
$2x = -4$
$x = -2$
So the x-intercept is $(-2, 0)$.

• y-intercept: Set $x=0$:

$y = -2(0) - 4 = -4$
So the y-intercept is $(0, -4)$.

Step3: Test a point for shading

Choose a test point not on the line, e.g., $(0,0)$:
$0 \leq -2(0) - 4$
$0 \leq -4$
This is false, so we shade the region not containing $(0,0)$ (the region below the line).

Answer:

1. Draw a solid line connecting the points $(-2, 0)$ and $(0, -4)$ (this is the line $y=-2x-4$).
2. Shade the entire region below this solid line.