What defines a linear inequality?

A linear inequality is defined primarily by the relationship it expresses between variables and how it is graphically represented. A key characteristic of a linear inequality is that it relates to a linear expression and, when graphed, it depicts a region in the coordinate plane that is typically bounded by a line.

When you have a linear inequality—such as those formulated in the standard form ( ax + by < c ) or ( ax + by \geq c )—the inequality indicates that not just points on the line defined by the equation ( ax + by = c ) satisfy the condition, but also all the points in one particular half-plane of the graph. This is what leads to the concept of a region, which can be shaded to represent all the solutions that satisfy the inequality.

The graph of a linear inequality can include the line itself (if the inequality is non-strict, like ( \leq ) or ( \geq )), or it can represent a portion of the plane that lies above or below the line (for strict inequalities, like ( < ) or ( > )). This region is what makes the answer about the graph being a region bounded by a line the correct choice, as it emphasizes the understanding of solutions