Graphing Linear Inequalities

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

The symbol ≤ indicates that the value on the left is less than or equal to the value on the right.

The symbol < indicates that the value on the left is less than the value on the right.

A solid line is used to graph inequalities with ≤ or ≥.

A dashed line is used to graph inequalities with < or >.

1. Graph the line $$y = \frac{1}{2}x - 3$$ with a dashed line. 2. Shade below the line to represent values less than the line.

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

Choose a test point not on the line (commonly (0,0)). If it satisfies the inequality, shade the side containing that point.

A linear equation shows equality (e.g., $$y = mx + b$$ ), while a linear inequality shows a relationship of less than or greater than.

It has a solid line representing the boundary and the area above the line is shaded.