Problem 63 - College Algebra

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 represents the points that are not included in the solution of the inequality. It means that the inequality does not include 'equal to'.

Step 1: Understanding the basics of graphing inequalities

When we graph inequalities, we often need to differentiate between possible values that are included in the solution or not. Graphically, this differentiation is made by using different line styles.

Step 2: Distinguishing between solid and dashed lines

A solid line in an inequality graph typically indicates the set of points that satisfies the inequality and are included in the solution, meaning the inequality includes 'equal to'. For example, in the inequality \(y \geq 2x + 1\), the line \(y = 2x + 1\) would be graphed as a solid line.

Step 3: Determining the meaning of dashed lines

On the other hand, a dashed line is used when the boundary line itself is not included in the solution set of the inequality. This is generally the case when the inequality does not include 'equal to'. For example, if we were to graph \(y > 2x + 1\), the line \(y = 2x + 1\) would be represented as a dashed line, indicating that the points on this line do not satisfy the inequality.