Graphing Inequalities in Two Variables

An inequality in two variables is a mathematical statement that compares two expressions using inequality symbols (like <, >, ≤, or ≥) and involves two variables, typically x and y.

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either greater than or equal to the value on the right side.

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either less than or equal to the value on the right side.

To graph $$y < -x + 2$$ , first graph the line $$y = -x + 2$$ as a dashed line (since it's a strict inequality). Then shade the area below the line to represent all the points where y is less than -x + 2.

To graph $$y ≤ -x + 2$$ , first graph the line $$y = -x + 2$$ as a solid line (since it's a non-strict inequality). Then shade the area below the line to represent all the points where y is less than or equal to -x + 2.

A dashed or dotted line is used for inequalities with < or > to indicate that the points on the line are not included in the solution.

A solid line is used for inequalities with ≤ or ≥ to indicate that the points on the line are included in the solution.

A solution to an inequality is any ordered pair (x, y) that makes the inequality true when substituted into the inequality.