The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

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WORKSHEET 4.12: GRAPHING LINEAR INEQUALITIES

IN THE COORDINATE PLANE

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Use the guidelines below for graphing inequalities:

• The symbol>means that all the points above the boundary line are solutions to the
  inequality. Draw a dotted boundary line and shade above it.


• The symbol≥means that all the points on the boundary line and the points above it
  are solutions to the inequality. Draw a solid boundary line and shade above it.


• The symbol<means that all the points below the boundary line are solutions to the
  inequality. Draw a dotted boundary line and shade below it.


• The symbol≤means that all the points on the boundary line and the points below it
  are solutions to the inequality. Draw a solid boundary line and shade below it.

EXAMPLE

Comparisons of the graphsy= 2 x+ 1 andy> 2 x+ 1.

y= 2 x+ 1 y> 2 x+ 1

DIRECTIONS: Graph each inequality.

1. y<x+ 2 2. y≥− 2 x


2. y ≤x 4. 2 y−x< 4

5.−y+x> 1 6.− 2 x+y≥ 4

7.x>y 8.x− 4 ≤y

CHALLENGE:Sam says thatx< 4 cannot be graphed because it is impossible

to shade below the graph ofx=4. Do you agree? Explain your reasoning.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.