Question

1. write an inequality for each graph.

Explanation:

Step1: Find line equation (slope-intercept)

First, identify two points on the line: $(0, -2)$ (y-intercept) and $(6, -5)$. Calculate slope:
$m = \frac{-5 - (-2)}{6 - 0} = \frac{-3}{6} = -\frac{1}{2}$
Slope-intercept form: $y = -\frac{1}{2}x - 2$

Step2: Determine inequality sign

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

Step3: Rewrite in standard form (optional, verify)

Multiply all terms by 2: $2y \leq -x - 2$, rearrange to $x + 2y \leq -2$

Answer:

$y \leq -\frac{1}{2}x - 2$ (or $x + 2y \leq -2$)