91Ó°ÊÓ

First, we can rewrite the inequality in slope-intercept form, which looks like: \(y = mx + b\). To do this, we need to isolate y: 1. Subtract x from both sides: \(3y \geq -x + 3\) 2. Divide by 3: \(y \geq -\frac{1}{3}x + 1\) Now, we need to graph this inequality. Since the inequality sign is greater than or equal to, we will use a solid line. Follow the steps below: 1. Plot the y-intercept (0, 1) on the coordinate plane. 2. From the y-intercept, use the slope to find another point on the line: slope = -1/3, so go down 1 unit and right 3 units from the y-intercept and make another point. 3. Draw a solid line to connect the points and extend it in both directions. 4. Choose a test point, e.g., (0, 0), and substitute it into the inequality: \(0 \geq -\frac{1}{3}(0) + 1\) which simplifies to \(-1 \geq 1\). This is false, so shade the region opposite to this test point.

Since the inequality sign is greater than or equal to, we will use a solid line. Follow the steps below: 1. Identify that x = -2 is a vertical line passing through all points with an x-coordinate of -2. 2. Draw a solid vertical line at x = -2. 3. Choose a test point, e.g., (0, 0), and substitute it into the inequality: \(0 \geq -2\). This is true, so shade the region including this test point.

On your graph, identify the area where the two shaded regions from both inequalities overlap. This intersecting area represents the solution to the compound inequality problem. Since we have "or" in between the inequalities, the final region includes the shaded regions from both inequalities.

Double-check your graph to ensure the lines, shading, and intersecting areas are correct. If everything is accurate, the graph is complete and represents the compound inequality \(x + 3y \geq 3\) or \(x \geq -2\).