Solving Linear Inequalities (Section 6
Sec 6.7 Graphing Linear Inequalities
Checking solutions: Tell whether the ordered pair is a solution of the inequality.
Ex 1) [pic] [pic] Ex 2) [pic] [pic]
A linear inequality will have a “boundary line”.
This line is the graph of the associated equation. .
Ex.
If your inequality contains [pic] or[pic], your boundary line must be____________.
(This indicates that all points on the line ________ solutions to the inequality)
If your inequality contains < or >, your boundary line must be ____________
(This indicates that points on the line ______________ solutions to the inequality.)
Follow the process below to graph a linear inequality:
Step 1: Graph the associated equation using any method you know. This is your boundary line.
If the original problem has [pic] or [pic], connect your points with a solid line.
If the original problem has < or >, connect your points with a dashed line.
Step 2: Determine which side of the line to shade by testing any point not on the line.
(0,0) is the easiest point to use ! (unless your line goes through the origin)
Substitute your test point into the original problem and see if it gives a True statement.
If so, shade over that point and all points on that side of the line.
If not, go to the other side of the line and shade those points.
Ex 3) Graph the inequality [pic].
Step 1: Graph the associated equation [pic]
Connect your points with a dashed line.
Step 2: Test (0,0) to see if it is a solution.
Shade all solutions!
Ex 4) Graph the inequality[pic].
Step 1:Graph the associated equation[pic]
Connect your points with a solid line.
Step 2: Test (0,0) to see if it is a solution.
Shade all solutions!
Ex 5) Graph the inequality [pic]
Ex 6) Graph the inequality [pic].
Ex 7) Graph the inequality [pic]
Ex 8) The graph of which inequality is shown?
a) [pic]
b) [pic]
c) [pic]
d) [pic]
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A linear inequality typically contains two variables and one of the following symbols: >, ................
................
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