Unit 1: Linear Functions and Inequalities Day 4:Linear Inequalities.

Slides:

Advertisements

Similar presentations

Solving Linear Inequalities

Advertisements

Solving Linear Inequalities

How to Graph a Linear Inequality. Linear Inequalities linear inequality  A linear inequality describes a region of the coordinate plane that has a boundary.

Warm Up Graph each inequality. 1. x > –5 2. y ≤ 0

Vocabulary Chapter 6.

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.

Systems of Linear Inequalities.  Two or more linear inequalities together form a system of linear inequalities.

Math Pacing Graphing 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.

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.

Objective Graph and solve linear inequalities in two variables.

Linear Equations in One Variable

Graphs of Linear Inequalities When the equal sign in a linear equation is replaced with an inequality sign, a linear inequality is formed. Solutions of.

3.4 Solving Systems of Linear Inequalities Objectives: Write and graph a system of linear inequalities in two variables. Write a system of inequalities.

Warm Up Graph each inequality. 1. x > – y ≤ 0.

Solving Linear Inequalities

+ Lesson 6-5 Linear Inequalities November 17, 2014.

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.

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.

Warm Up Graph each inequality. 1. x > –5 2. y ≤ 0

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

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.

2.8 Two-Variable Inequalities In some situations you need to compare quantities. You can use inequalities for situations that involve these relationships:

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.

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.

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.

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

Solving Systems of Equations Graphing Linear Inequalities.

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.

Solving Linear Inequalities

Solving Linear Inequalities

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

Warm Up Solve each inequality for y. 1. 8x + y < 6

Section 7.5 Systems of Linear Inequalities

Graphing Linear Inequalities

Graphing Linear Inequalities

Chapter 3 Graphs and Functions

Chapter 3 Section 5.

Agenda: Warm-Ups Go over yesterday’s quiz

Systems of Inequalities

Lesson Objective: I will be able to …

6.5 Solving Inequalities by Factoring

Day 8 – Linear Inequalities

Linear Inequalities in Two Variables

Solving Systems of 5-6 Linear Inequalities Warm Up Lesson Presentation

Warm Up Graph each inequality. 1. x > –5 2. y ≤ 0

Solving Linear Inequalities

Objective Graph Linear Equations and Linear Inequalities in Two Variables.

When you replace the equals sign in a linear equation by one of the inequality symbols, you now have a linear inequality. Examples: 1 2 y > x + 1 2x –

A system of linear inequalities is a set of two or more linear inequalities containing two or more variables. The solutions of a system of linear inequalities.

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

Learning Target Students will be able to: Graph and solve linear inequalities in two variables.

Solution of the Inequality

9 Chapter Chapter 2 Inequalities and Absolute Value.

Solving Linear Inequalities

When you replace the equals sign in a linear equation by one of the inequality symbols, you now have a linear inequality. Examples: 1 2 y > x + 1 2x –

Systems of Inequalities

Presentation transcript:

Unit 1: Linear Functions and Inequalities Day 4:Linear Inequalities

Learning Targets a) I can determine when an ordered pair is a solution to a linear inequality b) I can sketch the graph of a linear inequality c) I can write and solve a linear inequality for a real life situation

Linear Inequalities 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 ordered pair that makes the inequality true.

Linear Inequalities Tell whether the ordered pair is a solution of the inequality. Ex. (–2, 4); y < 2x + 1 Ex. (3, 1); y > x – 4

Linear Inequalities A linear inequality describes a region of a coordinate plane called a half-plane. All points in the region are solutions of the linear inequality. The boundary line of the region is the graph of the related equation.

Linear Inequalities

Graph the inequality. What type of boundary line should it have? Where would you be shading? The point (0, 0) is a good test point to use if it does not lie on the boundary line. Helpful Hint

Linear Inequalities Graph the inequality y  2x – 3 What type of boundary line should it have? Where would you be shading?

Linear Inequalities Graph the inequality 3x + 4y ≤ 12 What will you need to do first? What type of boundary line should it have? Where would you be shading?

Linear Inequalities Graph the inequality 4x - 3y > 2x + 6 What will you need to do first? What type of boundary line should it have? Where would you be shading?

Linear Inequalities Work time: WKST: Introduce a Hamburger WKST: Boy Tree – Girl tree

Linear Inequalities Wrap up EXIT QUIZ: Tell whether the ordered pair is a solution to the inequality. SHOW your work! 3. Graph the solution of the inequality