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Chapter 9: Problem 69

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

Short Answer

Expert verified
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. It is used when graphing 'greater than' or 'less than' inequalities.

Step by step solution

01

Understanding Graphs of Inequalities

In mathematics, when graphing inequalities, two types of lines are used: solid and dashed. The type of line used depends on the inequality sign in the equation.
02

The Meaning of Dashed Line

A dashed line is used when the inequality sign is either 'greater than' (>), or 'less than' (<). This is because the dashed line represents values that satisfy the inequality, but are not included within the solution set. In other words, a dashed line shows that the points on the line itself are not part of the solution to the inequality.
03

Application

For example, if we have an inequality like \(y > 2x + 3\), when we graph this inequality, all the points above the line \(y = 2x + 3\) are included in the solution, but the points on the line itself are not. That's why we use a dashed line to represent the line \(y = 2x + 3\).

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Most popular questions from this chapter

Graph the solution set of each system of inequalities or indicate that the system has no solution..\ \left\\{\begin{array}{l}2 x+y \leq 6 \\\x+y \geq 2 \\\1 \leq x \leq 2 \\\y \leq 3\end{array}\right.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The absolute value of any linear expression is greater than 0 for all real numbers except the number for which the expression is equal to \(0 .\)

Write each sentence as a linear inequality in two variables. Then graph the inequality. The \(y\) -variable is at least 2 more than the product of \(-3\) and the \(x\) -variable.

What is a solution of a system of linear inequalities?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \(|x|=-6\) is equivalent to \(x=6\) or \(x=-6\)
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