Graphing Linear Inequalities in Two Variables

Overview

Goal. Graph a linear inequality in two variables: draw its boundary line (solid when the line is included, dashed when it is not), then shade the half-plane of solutions, found by testing a point such as (0, 0).

Solution of a two-variable inequality (definition). An ordered pair (x, y) that makes the inequality true. Every such pair is one point in the shaded half-plane.

Boundary lines (solid or dashed), half-planes, and the test-point method.

Lesson Notes

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Lesson Video

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Interactive Activity

Goal. Use the explorer to study the boundary line of y = x + 1, then decide solid versus dashed, and use a test point to choose the shaded side.

Test point method. Substitute a point that is not on the boundary — (0, 0) when possible. If it makes the inequality true, shade its side; if false, shade the other side.

Graphing Linear Inequalities in Two Variables — Interactive ActivityOpen ›