Boundary Line
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A boundary line for a linear inequality is the line that represents the corresponding linear equation obtained by replacing the inequality sign with an equals sign. For example, in the inequality ax + by < c, the boundary line is given by the equation ax + by = c.
This line divides the coordinate plane into two regions: one where the inequality holds true and one where it does not. The region that satisfies the inequality is typically shaded. If the inequality is strict (using < or >), the boundary line is dashed, indicating that points on the line are not included in the solution set. If the inequality is inclusive (using < or >), the boundary line is solid, showing that points on the line are part of the solution set. The shading visually represents the set of all points that satisfy the inequality.