A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

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A linear inequality in two variables is an inequality that can be written in one of the forms:


A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

How to Graph Linear Inequalities in Two Variables:



(1) Replace the inequality symbol (A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY ) by an equal (A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY ) sign.


(2) Graph the resulting equation. Be sure to include the intercepts in the form (a,0) and (0,b) or the intercept (0,0) and a specific point (x,y).


(3) For A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY draw a dotted line. For A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY draw a solid line.

(4) Test a test point [usually (0,0) ] in the original linear inequality. If (0,0) is on the line choose (1,0) or any other point not on the line.

A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY If the original linear inequality is satisfied, shade in the direction of the test point. All the points (x,y) in the shaded area satisfy the original linear inequality.


A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY If the original linear inequality is not satisfied, shade in the opposite direction of the test point. All the points (x,y) in the shaded area satisfy the original linear inequality.


For systems of linear inequalities the solution is the overlap of the two or more shaded regions.



Study the examples presented in class as well as the examples on this handout.


(A) A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY
















(B) A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY


















(C) A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY


















(D) A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY














(E) A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

















(F) A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY
















(G) A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY


































(H) Graph the solution of the system of linear inequalities.

(A system of linear inequalities is two or more linear inequalities.)


A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY


























(I) Graph the solution of the system of linear inequalities.


A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

































(I) Graph the solution of the system of linear inequalities.

A LINEAR INEQUALITY IN TWO VARIABLES IS AN INEQUALITY

























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Tags: inequality in, linear inequality, inequality, variables, linear