Graphing Linear Inequalities
Aligned to A-REI.D.12 — Common Core State Standards for Mathematics.
What this lesson teaches
The solution to a linear inequality is a half-plane bounded by the line. Use a solid line for ≤ or ≥ and a dashed line for < or >, then shade the side that makes the inequality true.
Worked example
Graph y < 2x + 1. Draw y = 2x + 1 as a dashed line. Test (0, 0): 0 < 2(0) + 1 = 1 is true, so shade the side containing (0, 0).
Practice questions
- Should the boundary line for y ≥ x − 4 be solid or dashed? Why?
- Test whether (0, 0) satisfies y > x + 2.
- Describe the region that satisfies both y ≥ 0 and x ≥ 0.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Graficar Desigualdades Lineales
La solución de una desigualdad lineal es un semiplano limitado por la recta. Usa línea continua para ≤ o ≥ y línea punteada para < o >, luego sombrea el lado que hace verdadera la desigualdad.
Ejemplo: Grafica y < 2x + 1. Traza y = 2x + 1 como línea punteada. Prueba (0, 0): 0 < 2(0) + 1 = 1 es verdadero, así que sombrea el lado que contiene (0, 0).
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