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Chapter 7: Problem 91

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

Short Answer

Expert verified
In an inequality graph, a dashed line implies that the values on the line are not included in the solution set of the inequality. It's used for 'greater than' (>) or 'less than' (<) inequalities.

Step by step solution

01

Definition of Inequality

In the context of mathematics, an inequality is a relation between two expressions that may not be equal. It's often represented by symbols like '<', '>', '鈮�', '鈮�' etc.
02

Understanding the graphical representation of inequalities

When graphing inequalities, we use a dashed or solid line to distinguish between two scenarios. The line represents all the possible solutions to the inequality.
03

Deciphering the meaning of a dashed line

A dashed line is used when the values on the line are not included in the solution set of the inequality. Meaning, in the inequality 'y > f(x)' or 'y < f(x)', a dashed line indicates that the points actually on line y=f(x) are not solutions to the inequality.
04

Checking solutions for a dashed line inequality

To decide test points are solutions or not for an inequality represented by a dashed line, we choose the points not on the line, substitute them into the inequality. If the inequality holds true, then they are the solutions.

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Most popular questions from this chapter

a. Graph the solution set of the system: $$\left\\{\begin{array}{c}x \geq 0 \\\y \geq 0 \\\3 x-2 y \leq 6 \\\y \leq-x+7\end{array}\right.$$ b. List the points that form the corners of the graphed region in part (a). c. Evaluate \(2 x+5 y\) at each of the points obtained in \(\operatorname{part}(\mathrm{b})\)

Explain how to solve a nonlinear system using the addition method. Use \(x^{2}-y^{2}=5\) and \(3 x^{2}-2 y^{2}=19\) to illustrate your explanation.

Compare the graphs of \(3 x-2 y>6\) and \(3 x-2 y \leq 6\) Discuss similarities and differences between the graphs.

When graphing a linear inequality, I should always use \((0,0)\) as a test point because it's easy to perform the calculations when 0 is substituted for each variable.

What is a solution of a system of linear inequalities?
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