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Chapter 7: Problem 54

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

Short Answer

Expert verified
In the graph of an inequality, a dashed line represents a 'strict' inequality - (less than or more than). This implies that the boundary line (the dashed line) is not included in the solution set of the inequality.

Step by step solution

01

Understanding Line Types in Inequality Graphs

This is linked to one of the fundamental properties of inequalities. An inequality is either 'strict' or 'non-strict'. A 'strict' inequality is one that uses '<' (less than) or '>' (more than) symbols. A 'non-strict' inequality uses '<=' (less than or equal to) or '>=' (more than or equal to) symbols.
02

Interpreting Dashed Line in Inequality Graphs

In the graphical representation of inequalities, solid and dashed lines are used to distinguish between 'strict' and 'non-strict' inequalities. A dashed line is drawn when the inequality is a 'strict' one. This signifies that the boundary is not included in the solution set. In other terms, the solution contains values that are strictly more than or less than (but not equal to) a certain value.
03

Example for Further Understanding

For instance, consider the inequality 'y > 2x'. If you were to graph this inequality, you'd draw a dashed line along 'y = 2x', and shade the area above the line. This is because 'y > 2x' means that the solution set includes all points where the y-coordinate is strictly greater than twice the x-coordinate, but not equal to it.

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Most popular questions from this chapter

In Exercises 29-30, find the vertex for the parabola whose equation is given by writing the equation in the form \(y=a x^{2}+b x+c\). \(y=(x-3)^{2}+2\)

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x \leq 5 \\ y>-3\end{array}\right.\)

The figure shows the healthy weight region for various heights for people ages 35 and older. If \(x\) represents height, in inches, and y represents weight, in pounds, the healthy weight region can be modeled by the following system of linear inequalities: $$ \left\\{\begin{array}{l} 5.3 x-y \geq 180 \\ 4.1 x-y \leq 140 \end{array}\right. $$ Use this information to solve Exercises 45-48. Is a person in this age group who is 5 feet 8 inches tall weighing 135 pounds within the healthy weight region?

Graph each linear inequality. \(2 x+3 y>12\)

In Exercises 27-28, use the directions for Exercises 9-14 to graph each quadratic function. Use the quadratic formula to find \(x\)-intercepts, rounded to the nearest tenth. \(f(x)=-2 x^{2}+4 x+5\)
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