Download Graphing Linear Inequalities Notes

Algebra 2
Unit 2—Graphing Linear Inequalities Notes
Date: __________
An inequality is an expression that uses inequality symbols rather than an equal sign. In these
notes, we will review how to graph a single inequality, identify the solution region, and explain
what the solution region means. We will then graph a system of inequalities (2 or more), identify
the solution region, and explain what the solution region means.
*Remember that when you are solving an inequality for a variable, if you multiply or divide by a
negative number, that will change the direction of the inequality symbol.
 3x  6
2 x  4
Objective: I can graph a single linear inequality.
Graph each linear inequality:
Ex 1: y  3 x  4
Steps to graphing a linear inequality:
1. Solve for _____, if needed.
2. Graph the line using ____ and ____.
3. If using < or >, use a __________ line.
If using  or  , use a __________ line.
4. If using < or  , shade ________ the line.
If using > or  , shade ________ the line.
Ex 2: y 
3
x5
5
Not every line we need to graph will be in slope-intercept form. Graph each linear inequality
below.
Ex 3: Graph x  4
Ex 4: Graph y  2
If you have a vertical line:
*shade to the __________ for
< or 
*shade to the __________ for
> or 
If you have a horizontal line:
*shade __________ for
< or 
*shade __________ for
> or 
Ex 5: Graph 3x  2 y  10
Ex 6: 5 x  3 y  18
Example 7: Is the point (3, -1) a solution to the inequalities above? Explain why.
Ex 3:
Ex 4:
Ex 5:
Ex 6:
Objective 2: I can graph a system of linear inequalities.
Graphing 2 or more inequalities is exactly the same as graphing a single inequality, except the
solution will be the region that is double-shaded. The points in that region are solutions to BOTH
inequalities.
Graph each system below. Which quadrant(s) would have no solution?
3)
4)
Ex 5: Name one point in #3 that IS a solution _____________
Name one point in #3 that is NOT a solution _____________
6)