Problem 54 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

A dashed line in the graph of an inequality signifies that the points on the line are not included in the solution for that inequality. It represents 'less than' or 'greater than' inequalities, where the region of the solution does not include the boundary line.

Step 1: Understanding Solid and Dashed Lines

In the graph of an inequality, lines can be represented as either solid or dashed. The solid line represents an inequality that includes the points on the line itself, i.e., the inequality is either 'less than or equal to' or 'greater than or equal to'. The boundary line is included in the area of solution.

Step 2: Interpreting the Dashed Line in Graph

On the other hand, we represent the inequality with a dashed line when the points on the line are not included in the solution. This happens in case of 'less than' or 'greater than' inequalities. In such case, the boundary line is not part of the solution set.

Step 3: Illustrative Example

Consider a simple inequality y < 2x+1. If this inequality needs to be represented on a graph, the line established by y = 2x+1 would be a dashed line, showing that the points actually on this line are not included in the solution set of the inequality.