Graphing inequalities involves creating a boundary line, determining the shaded region based on inequality direction, and testing a point to confirm the solution set.
Graphing inequalities involves visually representing the solution set on a coordinate plane. Consider an inequality like (y > 2x - 1). Start by treating it as an equation and graph its boundary line (y = 2x - 1). Use a dashed line since the inequality is strict. Next, determine whether the shaded region is above or below the line. For (y > 2x - 1), shade the region above the line because it represents all points where (y) is greater than (2x - 1).
To find specific points in the shaded region, test a point not on the line, like the origin (0,0). Substitute its coordinates into the original inequality; if it's true, the shaded region includes the origin; if false, shade the opposite region. In this case, (0 > -1), confirming the region above the line.
For linear inequalities, solid or dashed lines represent greater than or equal to and less than or equal to, respectively. For systems of inequalities, shading overlaps where the solution sets intersect.