What should you do after graphing the line for an inequality?

After graphing the line for an inequality, shading the side that satisfies the inequality is essential because it visually represents all the solutions to that inequality on the graph.

When you graph a linear inequality, you start by graphing the corresponding linear equation (using a solid line if the inequality includes ≤ or ≥, and a dashed line if it includes < or >). The next step is to determine which side of the line represents the solutions to the inequality.

To find out which region to shade, you can choose a test point not on the line (usually the origin, (0,0), is a convenient choice). If the point satisfies the inequality, that side of the line indicates all solutions. If it does not, you shade the opposite side. This shading visually indicates the set of all possible solutions that satisfy the inequality, making it easier to interpret the graph in the context of the problem.

The other choices, while relevant to graphing or analyzing lines, do not directly pertain to the immediate next step after graphing an inequality. For example, plotting intercepts or labeling the slope serves a different purpose, and calculating the area of the feasible region can be a later consideration in optimization problems, rather than the immediate next step after establishing