Question

which graph show the linear inequality $3x + 3y \geq -6$
a. graph a
b. graph b
c. graph c
d. graph d
graph the solutions of the linear inequality $3x + 3y \geq -6$.

Explanation:

Step1: Rewrite inequality to slope-intercept form

Start with the given inequality:
$$3x + 3y \geq -6$$
Divide all terms by 3:
$$x + y \geq -2$$
Rearrange to solve for $y$:
$$y \geq -x - 2$$

Step2: Identify line type and intercepts

The inequality uses $\geq$, so the boundary line $y = -x - 2$ is solid (not dashed).

• y-intercept: When $x=0$, $y=-2$
• x-intercept: When $y=0$, $0 = -x -2 \implies x=-2$

Step3: Determine shaded region

Test the origin $(0,0)$ in the inequality:
$$0 \geq -0 -2 \implies 0 \geq -2$$
This is true, so the region containing the origin (above the line) is shaded.

Answer:

d. (The graph with a solid boundary line $y=-x-2$ and shading above the line, including the origin)