Problem 90 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

In the graph of an inequality, a solid line indicates that the points on the line are included in the solution of the inequality. It is usually used for 'greater than or equal to' or 'less than or equal to' inequalities.

Step 1: Understanding Inequalities and Their Graphs

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. An inequality can be represented on a number line, in which the numbers that make the inequality true are shaded or circled. Inequalities can also be represented on a xy-plane, often used when you have a two-variable inequality.

Step 2: Explaining Solid Lines

When graphing inequalities on a xy-plane, a solid line is used to represent a part of the graph where the points on the line are included in the solution of the inequality. This is usually the case for 'greater than or equal to' (\(>=\)) or 'less than or equal to' (\(<=\)) inequalities.

Step 3: Differentiating from Dashed Lines

In contrast, a dashed line is used when the points on the line are not included in the solution, applicable for 'greater than' (\(>\)) or 'less than' (\(<\)) inequalities. This differentiation is crucial to accurately understanding and interpreting graphed inequalities.