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Chapter 3: Problem 54

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 signifies that the points on the line are not included in the solution for that inequality. It represents 'less than' or 'greater than' inequalities, where the region of the solution does not include the boundary line.

Step by step solution

01

Understanding Solid and Dashed Lines

In the graph of an inequality, lines can be represented as either solid or dashed. The solid line represents an inequality that includes the points on the line itself, i.e., the inequality is either 'less than or equal to' or 'greater than or equal to'. The boundary line is included in the area of solution.
02

Interpreting the Dashed Line in Graph

On the other hand, we represent the inequality with a dashed line when the points on the line are not included in the solution. This happens in case of 'less than' or 'greater than' inequalities. In such case, the boundary line is not part of the solution set.
03

Illustrative Example

Consider a simple inequality y < 2x+1. If this inequality needs to be represented on a graph, the line established by y = 2x+1 would be a dashed line, showing that the points actually on this line are not included in the solution set of the inequality.

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Most popular questions from this chapter

determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. When I know that an equation's graph is a straight line, I don't need to plot more than two points, although I sometimes plot three just to check that the points line up.

Will help you prepare for the material covered in the first section of the next chapter. Determine the point of intersection of the graphs of \(2 x+3 y=6\) and \(2 x+y=-2\) by graphing both equations in the same rectangular coordinate system.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I have less than \(\$ 5.00\) in nickels and dimes, so the linear inequality $$0.05 n+0.10 d<5.00$$ models how many nickels, \(n,\) and how many dimes, \(d,\) that I might have.

Explain why \((5,-2)\) and \((-2,5)\) do not represent the same point.

How do you determine whether an ordered pair is a solution of an equation in two variables, \(x\) and \(y ?\)
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