LINEAR INEQUALITIES IN TWO VARIABLES - Copy.pptx

LINEAR INEQUALITIES IN TWO VARIABLES.pptx

1. WELCOME to our Math Class LEARNING MATH IS fun-tastic

2. MATHEMATICS 8 Quarter 2 Week 1 Linear Inequalities IN TWO VARIABLES Mr. Carlo Justino J. Luna MALABANIAS INTEGRATED SCHOOL Angeles City

3. LEARNING Competencies Differentiates linear inequalities in two variables from linear equations in two variables (M8L-IIa-2) Illustrates and graphs linear inequalities in two variables Solves problems involving linear inequalities in two variables (M8AL-IIa-4)

4. Initial Activity

5. GROUP ME!                     GROUP A GROUP B

6. GROUP A GROUP B GROUP ME!                    

7. GROUP ME!                     GROUP A GROUP B                     LINEAR EQUATIONS LINEAR INEQUALITIES

8. LINEAR INEQUALITIES IN TWO VARIABLES                     LINEAR EQUATIONS LINEAR INEQUALITIES LINEAR INEQUALITIES – less than – greater than – less than or equal to – greater than or equal to  

9. LINEAR INEQUALITIES Two linear expressions set that are separated by symbols , , ,   LINEAR INEQUALITIES IN TWO VARIABLES

10. A linear inequality in two variables can be written in four forms: where , , and are real numbers, and   LINEAR INEQUALITIES IN TWO VARIABLES

11. A linear inequality in two variables can be written in four forms: where , , and are real numbers, and   LINEAR INEQUALITIES IN TWO VARIABLES           Examples:

12. An ordered pair is a solution of a linear inequality in two variables if a TRUE statement results when the variables in the inequality are replaced by the coordinates of the ordered pair.   SOLUTION SET

13. SOLUTIONS OF AN INEQUALITY Determine whether each ordered pair is a solution of the given linear inequality.                     TRUE Therefore, is a solution of the given linear inequality.                 FALSE Therefore, is not a solution of the given linear inequality.        

14. SOLUTIONS OF AN INEQUALITY Determine whether each ordered pair is a solution of the given linear inequality.     TRUE Therefore, is a solution of the given linear inequality.       FALSE Therefore, is not a solution of the given linear inequality.       TRUE Therefore, is a solution of the given linear inequality.    

15. SOLUTIONS OF AN INEQUALITY Clearly, a linear inequality can have two or more solutions . While the graph of is a straight line , the graph of is a half-plane .   Linear Equation Linear Inequality The graph of a linear inequality in two variables is a HALF-PLANE . The shaded region consists of the points whose coordinates satisfy the inequality.

16. How do we graph linear inequalities in two variables? Linear Inequality The graph of a linear inequality in two variables is a HALF-PLANE . The shaded region consists of the points whose coordinates satisfy the inequality.

17. GRAPHING Linear Inequalities

18. Steps in Graphing Linear Inequalities in Two Variables Transform the linear inequality into linear equation . Determine the - and -intercept of the equation. Plot and draw the boundary line. Use dashed lines (------) if the inequality is or . However, graph using solid lines ( ) if the inequality is or , which means that the points on the line are included in the solution set. Use the given inequality to choose a test point to be substituted in the given inequality in order to identify the shaded side of the boundary line . It is advisable to use for easy substitution of values. If the resulting inequality is TRUE, shade the side that contains the test point. If the resulting inequality is FALSE, shade the other side of the boundary line.  

19. Example 1: Graph .     Rewrite the inequality as an equation. -intercept is .   Solve and plot the intercepts. -intercept is .   The boundary is a solid line since the inequality symbol is .  

20. Example 1: Graph .   TRUE   Pick a test point. Use if possible.   If the resulting inequality is TRUE , shade the side that contains the test point .

21. Example 2: Graph .     Rewrite the inequality as an equation. -intercept is .   Solve and plot the intercepts. There is no -intercept.   The boundary is a dashed line since the inequality symbol is .  

22. Example 2: Graph .   FALSE   Pick a test point. Use if possible.   If the resulting inequality is FALSE , shade the side that does not contain the test point .

23. Asynchronous / Self-Learning Activities Answer the following: Q2W1LC1A: What I Know What’s More What I Can Do Q2W1LC1B: What’s In What’s More (items 1 & 2 only) Google Forms link https://forms.gle/tiyr5aoZKo31v8aw8

24. MATHEMATICS 8 Quarter 2 Week 1 THANK You Mr. Carlo Justino J. Luna MALABANIAS INTEGRATED SCHOOL Angeles City