To graph linear inequalities, start by drawing the line in the same fashion as you would with a linear equation. A linear inequality has many solutions that can lie above or below the line described by the expression.
- Write out the statement defining the line representing the inequality
For example, use the inequality of y > 3x - 4. In slope-intercept form, this means the line has a slope of -3 and crosses the y-axis at (0, -4). Graph the line accordingly. However, because it is a greater-than symbol and not greater than or equal to, the line needs to be dotted. This represents the set of solutions edging infinitely close to the line without touching it.
- Test a point on the graph
For the simplest values, use the origin point of (0, 0) and substitute these values into the inequality. In this case, (0) > 3(0) - 4 does not hold true, so this point does not lie in the set of solutions. If the line crosses the origin point, you'll need to pick another point.
- Shade the region of the graph that contains a solution
Shading indicates that anywhere on the graph in the region contains points that satisfy the inequality. For multiple systems of inequalities, shade different patterns or different colors to avoid confusion.