Dashed Line

Definition

A dashed line is a type of line that is composed of a series of short line segments separated by gaps, rather than a continuous unbroken line. This visual representation is used in various mathematical and graphical contexts to convey specific meanings or properties.

5 Must Know Facts For Your Next Test

1. Dashed lines are used to represent the boundary of a linear inequality in a two-dimensional coordinate plane.
2. The dashed line indicates that the points on the line are not included in the solution set of the inequality, but the points on one side of the line are included.
3. When graphing a system of linear inequalities, dashed lines are used to represent the boundaries of the individual inequalities that make up the system.
4. The orientation of the dashed line (whether it is horizontal, vertical, or slanted) is determined by the coefficients of the variables in the linear inequality equation.
5. Dashed lines are often used in conjunction with solid lines to create a complete graphical representation of a system of linear inequalities.

Review Questions

• Explain the purpose of using a dashed line when graphing a linear inequality in two variables.
  • The dashed line is used to represent the boundary of a linear inequality in a two-dimensional coordinate plane. The dashed line indicates that the points on the line itself are not included in the solution set of the inequality, but the points on one side of the line are included. This visual representation helps to clearly distinguish the region that satisfies the given inequality.
• Describe how dashed lines are used when graphing a system of linear inequalities.
  • When graphing a system of linear inequalities, dashed lines are used to represent the boundaries of the individual inequalities that make up the system. The orientation of the dashed lines (horizontal, vertical, or slanted) is determined by the coefficients of the variables in the linear inequality equations. Dashed lines are often used in conjunction with solid lines to create a complete graphical representation of the system, where the region that satisfies all the inequalities is the intersection of the individual solution sets.
• Analyze the significance of the dashed line in the context of the properties of linear inequalities and their graphical representations.
  • The dashed line is a crucial visual cue in the graphical representation of linear inequalities. It conveys the idea that the points on the line itself are not part of the solution set, but the points on one side of the line are. This distinction is important because linear inequalities define a region in the coordinate plane, rather than a single line. The dashed line helps to clearly delineate the boundary of this region, allowing the viewer to easily identify the area that satisfies the given inequality. Understanding the meaning and significance of the dashed line is essential for interpreting and working with the graphical representations of linear inequalities and systems of linear inequalities.

Related terms

Solid Line:

A solid line is a continuous, unbroken line used to represent a distinct boundary or edge in a graph or diagram.

Inequality:

An inequality is a mathematical statement that compares two values using symbols such as greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤).

System of Linear Inequalities:

A system of linear inequalities is a set of two or more linear inequalities that must be satisfied simultaneously.