Linear Inequalities in Two Variables.  Tell whether each statement is true or false when x = -2 and y = 1: ◦ 2x – y < 5 TRUE ◦ x + 3y > 0 TRUE.

Slides:

Advertisements

Similar presentations

Linear Inequalities in 2 Variables

Advertisements

Graphing Linear Inequalities Section 3.4 MATH Mr. Keltner.

EXAMPLE 4 Graph a linear inequality in one variables Graph the inequality y  –3. SOLUTION Graph the equation y = –3. The inequality is , so use a solid.

9.3 Linear Inequalities in Two Variables. Objective 1 Graph linear inequalities in two variables. Slide

Graph linear inequalities with one variable EXAMPLE 2 Graph ( a ) y < – 3 and ( b ) x < 2 in a coordinate plane. Test the point (0,0). Because (0,0) is.

Graph linear inequalities with one variable EXAMPLE 2 Graph ( a ) y < –3 and ( b ) x < 2 in a coordinate plane. Test the point (0,0). Because (0,0) is.

6.5 Graphing Linear Inequalities in Two Variables Wow, graphing really is fun!

Graphing Linear Inequalities in Two Variables. Linear Inequalities A linear inequality in two variables can be written in any one of these forms:  Ax.

 Linear Equations in Two Variables  To Graph a Linear Inequality 1)Graph the related linear equality (forms the boundary line).  and  are graphed.

3.3 Linear Inequalities in Two Variables Objectives: Solve and graph a linear inequality in two variables. Use a linear inequality in two variables to.

6. 5 Graphing Linear Inequalities in Two Variables 7

A linear inequality is similar to a linear equation, but the equal sign is replaced with an inequality symbol. A solution of a linear inequality is any.

Graphing Inequalities of Two Variables Recall… Solving inequalities of 1 variable: x + 4 ≥ 6 x ≥ 2 [all points greater than or equal to 2] Different from.

Linear Equations in One Variable

2.6 Linear Inequalities in Two Variables

2.8 – Graph Linear Inequalities in Two Variables A linear inequality in two variables can be written in one of these forms: Ax + By < C Ax + By > C An.

Notes Over 2.6 Checking Solutions of Inequalities Check whether the given ordered pairs are solutions of the inequality.

Linear Inequalities in Two Variables Objectives: Solve and graph a linear inequality in two variables..

Chapter 6 – Solving and Graphing Linear inequalities

Graphing Linear Inequalities in Two Variables Section 6.5 Algebra I.

1 Warm Up 1.Solve and graph |x – 4| < 2 2. Solve and graph |2x – 3| > 1 2x – x 4 x – 4 > -2 and x – 4 < x > 2 and x < 6.

GRAPH LINEAR INEQUALITIES IN TWO VARIABLES January 22, 2014 Pages

EXAMPLE 2 Graph linear inequalities with one variable

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 10 Graphing Equations and Inequalities.

GOAL Graphing linear inequalities in two variables.

Do Now 1/5/12 In your notebook, explain how to graph the following line; y = 4x – 3 In your notebook, explain how to graph the following line; y = 4x –

Good Morning Systems of Inequalities. Holt McDougal Algebra 1 Solving Linear Inequalities Warm Up Graph each inequality. 1. x > –5 2. y ≤ 0 3. Write –6x.

Graphing linear Inequalities in 2 Variables. Checking Solutions An ordered pair (x,y) is a solution if it makes the inequality true. Are the following.

1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 2 3 Linear Inequalities in Two Variables Graph linear inequalities in two variables.

6-8 Systems of Linear Inequalities Select 2 colored pencils that blend together to produce a third distinct color! Algebra 1 Glencoe McGraw-HillLinda Stamper.

CHAPTER TWO: LINEAR EQUATIONS AND FUNCTIONS ALGEBRA TWO Section Linear Inequalities in Two Variables.

3.3 Linear Inequalities in Two Variables Objectives: Solve and graph a linear inequality in two variables. Use a linear inequality in two variables to.

Algebra 2 9/22/14 Bellwork:. 2.8 – Graph Linear Inequalities in Two Variables A linear inequality in two variables can be written in one of these forms:

Graphing Linear Inequalities in Two Variables A solution to a linear inequality is a point (x, y) that makes the inequality true. The solution set includes.

G RAPHING L INEAR I NEQUALITIES. L INEAR I NEQUALITIES A linear inequality in two variables can be written in any one of these forms:  Ax + By < C 

9.5 Inequalities in Two Variables  Two Key Terms  Two Objectives.

Drill Explain how to graph the following line; y = 4x – 3.

1.4 and 1.5 Graph Linear Inequalities in Two Variables/Systems of Linear Inequalities Inequalities Test: 2/26/10.

Graphing Linear Inequalities A linear inequality in two variables is an inequality that can be written in one of the following forms: A x + B y < C A x.

EXAMPLE 2 Graph a linear inequality in two variables Graph the inequality y > 4x – 3. STEP 2 0 > 4(0) – 3 ? Test (0, 0) in y > 4x – 3. SOLUTION Graph the.

Graphing Linear Inequalities in 2 Variables By Tristen Billerbeck.

1 Pottery How many bowls and vases can you make from a fixed amount of clay? You will see how a linear inequality can be used to answer this question.

2.6 Linear Inequalities in Two Variables A Linear Inequality in two variables is an inequality that can be written in one of the following forms: Ax +

2.8A Graphing Linear Inequalities. Table for inequality Graphing Line type Shading SolidDashed Above (right if ↕) ≥ > Below (left if ↕) ≤

Type Example Solution Linear equations 2x – 8 = 3(x + 5) A number in one variable x = -23.

§ 9.4 Linear Inequalities in Two Variables and Systems of Linear Inequalities.

Graphing Linear Inequalities

Chapter 3 Graphs and Functions

Graphing Linear Inequalities

2.8 Graph Linear Inequalities in Two Variables

Solving Systems of Linear Inequalities

Solving Linear Inequalities

Lesson 6.7 Graph Linear Inequalities in Two Variables

Solution Solution Checking Solutions of Inequalities

Graphing Linear Inequalities

Section 6.8 Linear Inequalities in Two Variables

Solving Linear Inequalities

Objective Graph and solve systems of linear inequalities in two variables.

Graphing Linear Inequalities

6-7 Graphing Inequalities in Two Variables

Graphing Linear Inequalities

Objective Graph and solve linear inequalities in two variables.

Solving Linear Inequalities

Objective Graph Linear Equations and Linear Inequalities in Two Variables.

Graph Linear Inequalities in Two Variables

4 minutes Warm-Up Solve and graph. 1) 2).

Tell whether the ordered pair is a solution of the equation.

Section 9.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities.

9 Chapter Chapter 2 Inequalities and Absolute Value.

Presentation transcript:

Linear Inequalities in Two Variables

 Tell whether each statement is true or false when x = -2 and y = 1: ◦ 2x – y < 5 TRUE ◦ x + 3y > 0 TRUE

New vocabulary: Linear inequality in two variables Half-plane

 Can be written in one of these forms where A, B, and C are constants: ◦ Ax + By < C ◦ Ax + By > C An ordered pair (x, y) is a solution of a linear inequality if the inequality is true when the values of x and y are substituted into the inequality.

 Check whether the given ordered pair is a solution of 2x + y < 5 a. (1,4)b. (2, -1)

 Check whether the given ordered pair is a solution of x – 3y > 4 a. (0, 0)b. (4, -1)c. (-2, -2)

 The graph of a linear inequality in two variables is the graph of all solutions of the inequality. The boundary line of the inequality divides the coordinate plane into two half-planes.  Shaded half-plane: points that are solutions  Non-shaded half-plane: contains the points that are not solutions

 A dashed line indicates that the points on the line are NOT solutions. ( >, < )  A solid line indicates that the points on the line ARE solutions. ( >, < )

 x > -1  y > 1  y < -3  x < 4

 Graph y < 2x in a coordinate plane  Graph 3x – 2y > 8 in a coordinate plane

 Graph the inequality in a coordinate plane: a. y > xb. y < -3xc. x + 2y < 6

p. 182 – even, 32-34, even, 44-46