key term - Solid Line

Definition

A solid line is a continuous, unbroken line used in graphing and visual representations to denote specific properties or relationships. In the context of linear inequalities and systems of linear inequalities, the solid line is a key element in accurately depicting the solution set.

5 Must Know Facts For Your Next Test

1. A solid line is used to represent the boundary line in the graph of a linear inequality or a system of linear inequalities.
2. The solid line indicates that the points on the line are included in the solution set, meaning they satisfy the inequality or system of inequalities.
3. The orientation of the solid line (horizontal, vertical, or slanted) depends on the coefficients and constants in the inequality or system of inequalities.
4. The solid line divides the coordinate plane into two half-planes, with the solution set occupying one of the half-planes.
5. In a system of linear inequalities, the solid lines representing the individual inequalities intersect to form the feasible region, which is the solution set for the entire system.

Review Questions

• Explain the purpose of a solid line in the graph of a linear inequality.
  • The solid line in the graph of a linear inequality represents the boundary line that separates the solution set from the non-solution set. The solid line indicates that the points on the line are included in the solution set, meaning they satisfy the inequality. The orientation of the solid line depends on the coefficients and constants in the inequality, and it divides the coordinate plane into two half-planes, with the solution set occupying one of the half-planes.
• Describe how a solid line is used in the graph of a system of linear inequalities.
  • In a system of linear inequalities, the solid lines representing the individual inequalities intersect to form the feasible region, which is the solution set for the entire system. The solid lines divide the coordinate plane into different regions, and the feasible region is the area where all the inequalities are satisfied. The solid lines indicate that the points on the boundary lines are included in the solution set.
• Analyze the role of a solid line in the context of the solution set for a linear inequality or a system of linear inequalities.
  • The solid line is a critical element in accurately depicting the solution set for a linear inequality or a system of linear inequalities. The solid line represents the boundary of the solution set, indicating that the points on the line are included in the solution. This allows for a clear visualization of the region that satisfies the inequality or system of inequalities. Understanding the significance of the solid line is essential in interpreting the solution set and making informed decisions based on the graphical representation of the problem.

Related terms

Linear Inequality:

A mathematical statement that shows the relationship between two or more variables, where one variable is less than, greater than, or equal to another variable.

Solution Set:

The set of all values that satisfy a given inequality or system of inequalities, represented graphically as the region on a coordinate plane.

Boundary Line:

The line that separates the solution set from the non-solution set in a linear inequality or system of linear inequalities.