1Cademy - Graphing $$y \geq -2x$$

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Graphing a Linear Inequality in Two Variables

Example

Graphing $y \geq -2x$

To graph the linear inequality $y \geq -2x$ , apply the standard three-step procedure. Step 1 — Graph the boundary line. Replace the $\geq$ symbol with an equal sign to find the boundary equation, $y = -2x$ . Because the inequality is non-strict ( $\geq$ ), draw this boundary as a solid line, indicating that all points on the line are included in the solution set. Step 2 — Test a point. The boundary line passes directly through the origin $(0, 0)$ , so the origin cannot be used as a test point. Select another point not on the line, such as $(1, 1)$ . Substituting $x = 1$ and $y = 1$ into the inequality yields $1 \geq -2(1)$ , which simplifies to the true statement $1 \geq -2$ . Thus, $(1, 1)$ is a valid solution. Step 3 — Shade the correct side. Since the test point $(1, 1)$ is a solution, shade the entire half-plane that contains this point, which is the region above and to the right of the solid boundary line.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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