Question

which is the graph of linear inequality $x - 2y \geq -12$?

Explanation:

Step1: Rewrite inequality to slope-intercept form

Start with $x - 2y \geq -12$. Isolate $y$:
$-2y \geq -x -12$
Multiply by $-1$ (reverse inequality):
$2y \leq x +12$
$y \leq \frac{1}{2}x +6$

Step2: Identify line properties

The boundary line is $y = \frac{1}{2}x +6$, which has a slope of $\frac{1}{2}$ and y-intercept $(0,6)$. Since the inequality is $\leq$, the line is solid, and we shade below the line.

Step3: Verify intercepts

Find x-intercept (set $y=0$):
$0 = \frac{1}{2}x +6 \implies x = -12$, so the line passes through $(-12,0)$ and $(0,6)$.

Step4: Match to graph

The graph with a solid line through $(-12,0)$ and $(0,6)$, and shading below the line is the top-left option.

Answer:

The top-left graph (with solid line through $(-12,0)$ and $(0,6)$, shading below the line)