Graph a two-variable linear inequality

Learning Objectives Identify the boundary line for a given two-variable linear inequality. Determine whether the boundary line should be solid or dashed based on the inequality symbol. Graph the boundary line on a coordinate plane accurately. Select an appropriate test point and use it to determine which half-plane to shade. Correctly shade the solution region on the coordinate plane. Interpret the graph as the set of all solutions to the inequality. Ever wondered how many songs you can download and how many videos you can stream without exceeding your data limit? 📱 Graphing inequalities helps you see all your options at once! This tutorial will guide you through the process of graphing two-variable linear inequalities. You'll learn how to turn an inequality into a vi...

TermDefinitionExample Linear Inequality in Two VariablesA mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥), where at least one expression contains two variables (like x and y) raised to the power of 1.y < 2x + 5 or 4x - 3y ≥ 12 Boundary LineThe line that separates the coordinate plane into two regions, or half-planes. It represents the 'equals' part of the inequality.For the inequality y > x - 3, the boundary line is the equation y = x - 3. Half-PlaneOne of the two regions of the coordinate plane created by the boundary line. All the points in one half-plane are solutions to the inequality, while the points in the other are not.The graph of y > x - 3 has a boundary line y = x - 3, which divides the plane into an upper ha...

Boundary Line Type For inequalities with > or <, use a DASHED line. For inequalities with ≥ or ≤, use a SOLID line. A dashed line shows that the points on the line are NOT part of the solution. A solid line shows that the points on the line ARE part of the solution. Test Point Method for Shading 1. Choose a point not on the line (e.g., (0,0)). 2. Substitute its coordinates into the original inequality. 3. If the result is TRUE, shade the half-plane containing the test point. 4. If the result is FALSE, shade the other half-plane. This is the most reliable method to determine which region represents the solution set. Always use the original inequality for the test to avoid errors from rearranging the equation.