The problem asks to graph the linear inequality $y \ge \frac{1}{3}x - 2$.

1. Problem Description

The problem asks to graph the linear inequality $y \ge \frac{1}{3}x - 2$.

2. Solution Steps

First, we need to identify the slope and y-intercept of the linear equation.

The inequality is in slope-intercept form $y \ge mx + b$, where $m$ is the slope and $b$ is the y-intercept.

In the inequality $y \ge \frac{1}{3}x - 2$, we have $m = \frac{1}{3}$ and $b = -2$.

This means the line has a slope of $\frac{1}{3}$ and a y-intercept of $-2$.

To graph the line, we start by plotting the y-intercept at the point $(0, -2)$.

Next, we use the slope to find another point on the line. Since the slope is $\frac{1}{3}$, we can go up 1 unit and right 3 units from the y-intercept to find another point.

So, from $(0, -2)$, we move up 1 to $-1$ and right 3 to $3$, giving us the point $(3, -1)$.

We can draw a line through these two points.

Since the inequality is $\ge$, we use a solid line to indicate that the points on the line are included in the solution.

Now, we need to determine which side of the line to shade. Since the inequality is $y \ge \frac{1}{3}x - 2$, we shade the region above the line.

Any point in the shaded region represents a solution to the inequality.

3. Final Answer

The graph of the inequality $y \ge \frac{1}{3}x - 2$ is a solid line with a slope of $\frac{1}{3}$ and a y-intercept of $-2$, and the region above the line is shaded. I cannot draw the graph here, but the description above explains how to draw the graph.