1. 6-7 Graphing Inequalities in Two Variables
Today you will need graph paper, a colored pencil, and a ruler.
Algebra Glencoe McGraw-Hill Linda Stamper

2. Graphing A Linear Inequality
The graph of a linear inequality in two variables is the graph of the solutions of the inequality.
A boundary line divides the coordinate plane into two half-planes. x
The solution of a linear inequality in two variables is a half-plane. Shade the side of the half-plane that contains the solutions.

3. Graphing A Linear Inequality
The graph of a linear inequality in two variables is the graph of the solutions of the inequality.
A boundary line divides the coordinate plane into two half-planes. x
The solution of a linear inequality in two variables is a half-plane. Shade the side of the half-plane that contains the solutions.

4. Graphing A Linear Inequality
Use a dashed boundary line for < or >. A dashed line indicates that the points on the line are NOT solutions. x
Use a solid boundary line for < or >. A solid line indicates that the points on the line are solutions.

5. Graphing A Linear Inequality
Graph the corresponding equation, using a dashed
line (< or >) or a solid line ( < or >) to construct the boundary line. You may need to write the equation in slope-intercept form.
2. Test the coordinates of a point in one of the half-planes. You can use any point that is not on the line as a test point.
3. Shade the half-plane containing the test point if it is a solution of the inequality. If it is not a solution, shade the other half-plane.
Graphing A Linear Inequality

6. Check whether the ordered pair (–2,3) is a solution of the inequality.
(x,y)
Write the inequality.
Substitute values given in the ordered pair.
Simplify.
solution
If statement is true, then the ordered pair is a solution.
If statement is false, then the ordered pair is not a solution.

7. Check whether the ordered pair is a solution of the inequality .
Example 1 (0,2)
Example 2 (–3,5)
Example 3 (0,0)
solution
solution
not a solution
Which ordered pair was easiest to check?

8. Graphing A Linear Inequality
Graph the corresponding equation, using a dashed
line (< or >) or a solid line ( < or >) to construct the boundary line. You may need to write the equation in slope-intercept form.
2. Test the coordinates of a point in one of the half-planes. You can use any point that is not on the line as a test point.
3. Shade the half-plane containing the test point if it is a solution of the inequality. If it is not a solution, shade the other half-plane.
Graphing A Linear Inequality

9. Great to use as a test point because it’s easy to calculate!
Check whether the ordered pair is a solution of the inequality
Example 1 (0,2)
Example 2 (–3,5)
Example 3 (0,0)
solution
solution
not a solution
Which ordered pair was easiest to check?
Great to use as a test point because it’s easy to calculate!

10. Graphing A Linear Inequality
Graph the corresponding equation, using a dashed
line (< or >) or a solid line ( < or >) to construct the boundary line. You may need to write the equation in slope-intercept form.
2. Test the coordinates of a point in one of the half-planes. You can use any point that is not on the line as a test point.
3. Shade the half-plane containing the test point if it is a solution of the inequality. If it is not a solution, shade the other half-plane.
Graphing A Linear Inequality

11. Use the inequality to test the point!
Graph the inequality.
Write the related equation (boundary line). •
Write in slope-intercept form. x • •
Graph the equation.
Use a solid line.
Test a point. Use (0,0) if possible. y
Test is a solution, so shade half-plane that contains the test point.
Use the inequality to test the point!
solution

12. Use the inequality to test the point!
Graph the inequality.
x > 2
Write the related equation.
boundary line • x
Graph the equation.
Use a dashed line.
Test a point.
Use (0,0) if possible. y
Test is false (not a solution), shade half-plane that does not contain the test point.
false
not a solution
Use the inequality to test the point!

13. Please copy all of the above problems in your spiral notebook!
Graph each inequality.
Ex. 4
Ex. 5
Ex. 6
Ex. 7
Ex. 8
Ex. 9
Please copy all of the above problems in your spiral notebook!

14. Use the inequality to test the point!
Example 4 Graph the inequality. y
y > – 3
boundary line • x
solution
Use the inequality to test the point!

15. Use the inequality to test the point!
Example 5 Graph the inequality. y
boundary line • • x •
Use the inequality to test the point!
solution

16. Example 6 Graph the inequality.
boundary line • • x •
not a solution

17. Example 7 Graph the inequality.
boundary line • • x •
solution

18. Example 8
Example 9 • • • x • x • y y

19. Homework
6-A13 Pages 337–339 # 8–17,27–30,33-36,48-50.