Question

1. write an inequality for each graph.

Explanation:

Step1: Find line slope-intercept form

First, identify two points on the line: $(-2, 0)$ and $(0, -4)$. Calculate slope:
$m = \frac{-4 - 0}{0 - (-2)} = \frac{-4}{2} = -2$
The y-intercept $b = -4$, so line equation is $y = -2x - 4$.

Step2: Determine inequality symbol

The line is solid, so use $\leq$ or $\geq$. The shaded region is below the line, so use $\leq$.

Step3: Finalize the inequality

Substitute into the inequality form:
$y \leq -2x - 4$
We can rearrange to standard form:
$2x + y \leq -4$

Answer:

$y \leq -2x - 4$ (or $2x + y \leq -4$)