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

Teaching Notes 4.12: Graphing Linear Inequalities

in the Coordinate Plane

Once students have mastered graphing equations in the coordinate plane, they are ready to graph

linear inequalities. Deciding whether to make a solid line or a dotted line and shading the correct

part of the graph often prove to be problem areas.

1. Explain the basic steps for graphing a linear equation. Especially note the following:
   
   
   • Students may use thex-andy-intercepts to graph a linear equation or they may graph
     they-intercept and then move vertically and horizontally, depending on the slope, to
     graph the second point.
   
   
   • Students should draw a line connecting the points, understanding that all solutions to
     the equation are on the line.
   
   
   
   


2. Note that the graph of a linear equation separates the coordinate plane into three parts: a set
   of points above the line, the points on the line, and the points below the line. The graph of
   a linear inequality is shown by shading the portion of the coordinate plane that is above or
   below the line. The boundary line may or may not be a part of the graph.


3. Review the information and example on the worksheet with your students, particularly the
   meaning of the inequality symbols as they apply to graphing.

EXTRA HELP:

Select a point in the portion of the graph that you have shaded to be sure it is a solution of the

inequality. If it is not a solution, shade the other portion of the graph.

ANSWER KEY:

Thex-intercept,y-intercept, and a description of the graph are provided.

(1)(−2, 0); (0, 2); dotted line, shaded below (2)(0, 0); (0, 0); solid line, shaded above

(3)(0, 0); (0, 0); solid line, shaded below (4)(−4, 0); (0, 2); dotted line, shaded below

(5)(1, 0); (0,−1); dotted line, shaded below (6)(−2, 0); (0, 4); solid line, shaded above

(7)(0, 0); (0, 0); dotted line, shaded below (8)(4, 0); (0,−4); solid line, shaded above

------------------------------------------------------------------------------------------

(Challenge)Disagree. The graph ofx<4 is a dotted vertical line that crosses thex-axis at (4, 0).

The solutions to this inequality include all the values to the left of the line.

------------------------------------------------------------------------------------------

160 THE ALGEBRA TEACHER’S GUIDE