Graphing a linear inequality is just an extension of graphing a straight line!
graphline2
definition
An inequality written in the form Ax + By < C (where A and B are not zero), is called a linear inequality in two variables.

bullet Steps for Graphing a Linear Inequaltiy

• Isolate y to one side of the inequality (if necessary).

• Replace the inequality symbol with an = sign to create an equation.

Graph the straight line of the equation. (This will be the boundary line of the inequality graph.)

• Draw the line dashed if you have a "strict" inequality (less than or greater than).

• Draw the line solid if the inequality is less than or equal to or greater than or equal to.

Choose a point not on the line as a test point. The point (0,0) is an easy point to test, as long as it is not on the line. The test point will lie in one of the half-planes formed by the boundary line.

• If the test point makes the inequality true, shade that side of the line (shading over the point). If the test point makes the inequality false, shade the other side of the line (not shading over the point).


ex1 Graph the inequality gl1

1. The inequality already has y isolated.

2. Graph the straight line y = 2x - 4. The line is drawn solid since the inequality is greater than or equal to.

3. Pick a test point not on the line.
The point (0,0) was used in this example.

4. Check the test point:
gl2at

5. The test point gave a true result, so the graph is shaded on that side of the line (so that the shade will cover the test point).

gl2a

dash

ex2 Graph the inequality   4y < -2x - 12

1. Isolate the y value. Divide all terms by 4.
y < - ½ x - 3

2. Graph the straight line y = -½ x - 3. The line is drawn dashed since this is a strict inequality (less than).

3. Pick a test point not on the line.
The point (0,0) was used in this example.

4. Check the test point:
0 < -½ (0) - 3
0 < -3   false

5. The test point gave a false result, so the graph is shaded on other side of the line (so that the shade will NOT cover the test point).

inqesamplegraph2

dash

reminder The graph of a linear inequality is always a "region" of the
plane (a "half-plane") bounded by a straight line.

dash 

ti84c
How to use your
TI-83+ graphing calculator  to graph linear inequalities.
Click calculator.



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