which is the graph of linear inequality x - 2y ≥ -12?

Explanation:

Step1: Rewrite the inequality in slope - intercept form

First, rewrite $x - 2y\geq - 12$ as $y\leq\frac{1}{2}x + 6$. We get this by subtracting $x$ from both sides ($-2y\geq -x - 12$) and then dividing by $- 2$ (and reversing the inequality sign since we divide by a negative number).

Step2: Analyze the boundary line

The boundary line of the inequality $y\leq\frac{1}{2}x + 6$ is the equation $y=\frac{1}{2}x + 6$. The slope of the line is $\frac{1}{2}$ and the y - intercept is 6. Since the inequality is $\leq$, the boundary line is solid.

Step3: Test a point

We can test the point $(0,0)$. Substitute $x = 0$ and $y = 0$ into the original inequality $x-2y\geq - 12$. We have $0-2\times0=0\geq - 12$, which is true. So, the region that contains the origin $(0,0)$ is the solution region.

Answer:

The graph with a solid line having a slope of $\frac{1}{2}$ and y - intercept of 6, and the region below (and including) the line and containing the origin.