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Chapter 9: Problem 68

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

Short Answer

Expert verified
In the graph of an inequality, a solid line signifies that all the points on the line are included in the solution of the inequality. This gives life when the inequality is 'less than or equal to' or 'greater than or equal to'.

Step by step solution

01

Understand the role of a line in a graph

In the context of graphing, a line usually represents a mathematical relationship between two variables. A line can either be solid or dashed to portray different meanings.
02

Explore the meaning of a solid line

When graphing an inequality, the line drawn is usually solid if the inequality is 'less than or equal to' or 'greater than or equal to'. The solid line represents that all points on the line are included in the solution of the inequality.
03

Use of solid line in an example

Let's consider an inequality \(y \geq 2x + 1\). When this inequality is graphed, a solid line will be drawn because the inequality includes 'equal to' sign. Any point on this line also fulfills the condition \(y \geq 2x + 1\)

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Most popular questions from this chapter

Explain how to solve a compound inequality involving or.

Solve each inequality using a graphing utility. Graph each of the three parts of the inequality separately in the same viewing rectangle. The solution set consists of all values of \(x\) for which the graph of the linear function in the middle lies between the graphs of the constant functions on the left and the right. $$1 \leq 4 x-7 \leq 3$$

Simplify: \(4-[2(x-4)-5] .\) (Section 1.8, Example 11)

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