Problem 91 - College Algebra

Question

What does a dashed line mean in the graph of an inequality?

Step-by-Step Solution

Answer

A dashed line in a graph of an inequality signifies that the points on the line itself are not included in the solution set of the inequality. It is used for 'less than' or 'greater than' relations.

Step 1: Understanding Graphs for Inequalities

When graphing inequalities, a line is used to visually distinguish two sections of a graph. These sections would be the set of points that satisfy the inequality, versus the set that does not. A dashed or a solid line is drawn based on whether or not the points on that line meet the inequality's conditions. The graph will include a shaded region, which represents all the solutions to an inequality.

Step 2: Understanding Dashed Lines

A dashed line in the graph of an inequality means the points lying on the line itself are not included in the solution of the inequality. It is used when the inequality is 'less than' or 'more than', but not 'more than or equal to' or 'less than or equal to'. The dashed line just represents the boundary between the solutions and non-solutions, but doesn't include any solutions itself.

Step 3: Application

For instance, when graphing the inequality \(y > 2x + 1\), it would be represented by a dashed line because points on the line \(y = 2x + 1\) don't satisfy the inequality. The shaded region (representing the solution) would be the part of the graph above this boundary line.