Problem 90 - College Algebra

Question

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

Step-by-Step Solution

Answer

A solid line in the graph of an inequality indicates that the inequality is a 'less than or equal to' or a 'greater than or equal to' inequality. It means that the points lying on the line as well are part of the solution to the inequality.

Step 1: Understand the Graphical Representation of Inequalities

In a graph, inequalities are usually represented with lines. The nature of these lines, whether they are solid or dashed, is not random but holds certain meaning in terms of the inequality it represents. Inequalities can be classified as either strict (less than, greater than) or non-strict (less than or equal to, greater than or equal to).

Step 2: Define the Meaning of a Solid Line

A solid line represents a set of points which fulfills the equation of the line. This is used when graphing non-strict inequalities. The solid line suggests that the points on that line are included in the solution of the inequality. In other words, if you substitute the coordinates of any point on the solid line into the inequality, it would make the inequality true.

Step 3: Interpret the Solid Line in an Inequality

So, when a solid line is used in the graph of an inequality, it implies that the inequality is either 'greater than or equal to' or 'less than or equal to' type. Therefore, all the points on the line are solutions to the inequality problem.