Problem 91 - Algebra and Trigonometry

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 indicates that the points on the line are not included in the solution set of the inequality.

Step 1: Introduction to inequalities on a graph

While graphing inequalities on a two-dimensional plane, a line (either solid or dashed) is used to represent the equation associated with the inequality. The area delimited by that line represents the solution set of the inequality.

Step 2: Significance of dashed line

A dashed line on the graph of an inequality indicates that the points on that line are not included in the solution set of the inequality. Typically, inequalities with 'greater than' (>) or 'less than' (<) symbols use dashed lines to graphically represent the inequality.

Step 3: Comparison with solid line

On the other hand, a solid line indicates that the points on that line are included in the solution set of the inequality. Inequalities with 'greater than or equal to' (≥) or 'less than or equal to' (≤) symbols use solid lines for representation.