Linear Inequality Graphing Calculator
Visualize the solution set for linear inequalities in the form y < mx + b
Understanding Linear Inequalities
A linear inequality looks similar to a linear equation, but instead of an equals sign, it uses an inequality symbol such as <, ≤, >, or ≥. While a linear equation graphs as a straight line, a linear inequality graphs as a region of the coordinate plane.
How to Use This Calculator
To graph an inequality, you need to identify the slope ($m$) and the y-intercept ($b$) of the boundary line. Enter these values into the calculator along with the inequality sign. The tool will draw the boundary line and shade the appropriate region representing the solution set.
Solid vs. Dashed Lines
The boundary line of the graph changes based on the inequality symbol:
- Solid Line (≤ or ≥): Points on the line are solutions to the inequality.
- Dashed Line (< or >): Points on the line are not solutions; only the shaded area is valid.
Shading the Solution Set
The shading indicates which side of the boundary line contains the solutions. If the inequality is $y > mx + b$, we shade above the line. If it is $y < mx + b$, we shade below the line. This calculator automatically determines the correct shading based on your inputs.