30S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Graphing Inequalities in.

Slides:

Advertisements

Similar presentations

Graphing Linear Inequalities in Two Variables

Advertisements

Solve Systems of Equations & Graph Inequalities

Graphing a Linear Inequality in Two Variables Replace the inequality symbol with an equal sign and graph the corresponding linear equation. Draw a solid.

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!

Warm Up Graph each inequality. 1. x > –5 2. y ≤ 0 3. Write –6x + 2y = –4 in slope-intercept form, and graph. y = 3x – 2.

Kristie Ferrentino. 1. Find and graph the solution set of the inequality. 2. Determine the equation of a line that passes through the point (2,6) and.

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

Math Pacing Graphing Inequalities in Two Variables.

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.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 8 Systems of Equations and Inequalities.

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.

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.

30S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Systems of Linear Equations Lesson: SLE-L1 Intro to Systems of Linear Equations Find x 3(x.

Systems of Inequalities. Graphing a Linear Inequality in Two Variables 1.Replace the inequality symbol with an equal sign and graph the corresponding.

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.

Graphing and solving systems of linear inequalities.

GOAL Graphing linear inequalities in two variables.

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.

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

Drill #25 1. Find the slope intercept equation of the lines a.) parallel to and b.) perpendicular to y = ¾x + 1 passing through (6,2) 2. Find the standard.

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.

1.4 Graphing linear Inequalities in Two Variables Pg.17.

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.

“Where the Points Lie” Systems of Linear Inequalities.

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.

Lesson 2.11 Solving Systems of Linear Inequalities Concept: Represent and Solve Systems of Inequalities Graphically EQ: How do I represent the solutions.

Chapter 3 Section 5. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Graphing Linear Inequalities in Two Variables Graph linear inequalities.

Graphing a Two Variable Inequality. Examining the Solutions of a Linear Equation Are the following points solutions to the equation y = -2x + 3 ? Justify.

Pre-Algebra 11-6 Graphing Inequalities in Two Variables 11-6 Graphing Inequalities in Two Variables Pre-Algebra Warm Up Warm Up Problem of the Day Problem.

Systems of Inequalities Essential Question: How do we solve systems of inequalities by graphing? Standard: MCC9-12.A.REI.12.

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.

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.

Lesson 2.8 Graph Linear Inequalities in Two Variables.

Solving Absolute Value Equations & Inequalities Solving Absolute Value Equations & Inequalities.

6-5: Linear Inequalities Day 1. Graphing Inequalities in the Coordinate Plane When a line is drawn in a plane, the line separates the plane into __________.

Warm-up: Solve for x. 6x + 12 = x 2x + 3(x – 5) = 25

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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

Chapter 3 Graphs and Functions

Graphing a Linear Inequality in Two Variables

Graphing Linear Inequalities

2.8 Graph Linear Inequalities in Two Variables

Objective solve systems of linear inequalities in two variables.

Lesson 6.7 Graph Linear Inequalities in Two Variables

2.6 Graphing linear Inequalities in 2 Variables

Section 6.8 Linear Inequalities in Two Variables

Systems of Inequalities

Linear Inequalities in Two Variables

Solutions of Equations and Inequalities

Objective Graph and solve linear inequalities in two variables.

Solving Systems of Linear Inequalities

Objective Graph Linear Equations and Linear Inequalities in Two Variables.

Graphing Linear Inequalities in 2 Variables

1.4 Graphing linear Inequalities in Two Variables

2-8: Two Variable Inequalities

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

9 Chapter Chapter 2 Inequalities and Absolute Value.

Systems of Inequalities

Presentation transcript:

30S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Graphing Inequalities in Two Variables Learning Outcome B-1 LP-L2 Objectives: Graph a linear inequality in two variables on a Cartesian Plane

30S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables When you place a line on a coordinate plane, the line creates three regions: the region that is the line itself the region to the left of the line the region to the right of the line Consider the graph of the equation y = 2x + 1 shown. It separates the coordinate plane into two half-planes. One half-plane, Region 1, is on the left of the line. The point A with coordinates (-4, 3) is in Region 1. Theory – Inequalities in Two Dimensions

30S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables If the x-coordinate of point A, -4, is substituted into the equation of the line to find the corresponding y-coordinate on the line, the result is: y = 2x + 1 y = 2(-4) + 1, or y = -7. In other words, the y-value for the point A is greater than the y- value for the line. Use another point in Region 1 to verify the relationship. The y- values in Region 1 for a given x-value are greater than the y-values on the line. This region or half-plane can be represented by the inequality y > 2x + 1. Theory – Inequalities in Two Dimensions

30S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables What inequality do you think represents the area in Region 2? The other half-plane (Region 2) is on the right of the line. The point B with coordinates (2, 2) is in Region 2. If the x-coordinate of point B, 2, is substituted into the equation of the line to find the corresponding y-coordinate on the line, the result is: y = 2x + 1 y = 2(2) + 1, or y = 5. In other words, the y-value for the point B is less than the y- value for the line. The y- values in Region 2 for a given x- value are less than the y-values on the line. This region or half-plane can be represented by the inequality y < 2x + 1. Theory – Inequalities in Two Dimensions

30S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Summary A line divides the coordinate plane into two half-planes, which can each be represented by an inequality statement. In our example, the line y = 2x + 1 divides the coordinate plane into two halves. Given the line’s positive slope, the left half can be represented by the equation y > 2x + 1, and the right half can be represented by the equation y < 2x + 1. Theory – Inequalities in Two Dimensions

30S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Example Graph the region 2x + y < 4. Steps: 1.Solve for y. 2.Determine dashed or solid line. 3.Select a point and test in inequality. 4.Shade accordingly. (If test was true, shade region that includes point. If false, shade other side of boundary.) Example – Inequalities in Two Dimensions

30S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Example Graph the region 2x + y < 4. Solution Example – Inequalities in Two Dimensions

30S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Graph the region: Test Yourself

30S Applied Math Mr. Knight – Killarney School Slide 9 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Graph the region: Test Yourself

30S Applied Math Mr. Knight – Killarney School Slide 10 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Graph the region: Test Yourself

30S Applied Math Mr. Knight – Killarney School Slide 11 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Graph the region: Test Yourself

30S Applied Math Mr. Knight – Killarney School Slide 12 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Graph the region: Test Yourself

30S Applied Math Mr. Knight – Killarney School Slide 13 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Special Case: Graph the region: Test Yourself

30S Applied Math Mr. Knight – Killarney School Slide 14 Unit: Linear Programming Lesson: Graphing Inequalities in Two Variables Special Case: Graph the region: Test Yourself