Which graph best represents the solution set of y - (1/2)x ≥ 4?

To determine which graph best represents the solution set of the inequality y - (1/2)x ≥ 4, we must first understand the inequality itself and how to graph it.

Step 1: Rearrange the inequality to the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

y >= (1/2)x + 4

Step 2: Plot the y-intercept (0,4) on the graph. This is the point where the line will cross the y-axis.

Step 3: Use the slope to find another point. Since our slope is 1/2, from the y-intercept, you'd go up 1 unit and right 2 units to find a second point. Plot this second point on the graph.

Step 4: Draw a solid line through these two points because the inequality includes equality (≥), meaning points on the line are included in the solution.

Step 5: Determine which side of the line to shade. To do this, take a test point that's not on the line, like (0,0), and plug it into the inequality.

y - (1/2)x >= 4 becomes 0 - (1/2)(0) >= 4, which simplifies to 0 >= 4. This statement is false, so the area that includes (0,0) is not part of the solution set. Thus, you need to shade the opposite side of the line, which is the side where y-values are greater (above the line).

The correct graph is a solid line through the points (0,4) and (2,5) with the region above the line shaded.