Graph and solve systems of linear inequalitites A-CED 3.

Slides:

Advertisements

Similar presentations

2.1 Lines and Slopes. Example 1: Find the Slope Possibilities for a Line’s Slope.

Advertisements

Preview Warm Up California Standards Lesson Presentation.

Do Now Find the slope of the line passing through the given points. 1)( 3, – 2) and (4, 5) 2)(2, – 7) and (– 1, 4)

Splash Screen Chapter 9 Lesson A 2.B 3.C 4.D Solve the inequality –2x ≤ 5. Then check your solution. (over Chapter 8) A. B. C. D.

Slope-Intercept and Point-Slope Forms of a Linear Equation.

Lesson 7.5, page 755 Systems of Inequalities Objective: To graph linear inequalities, systems of inequalities, and solve linear programming problems.

{ Graphing Linear Equations And Inequalities.  Create an x y chart.  Pick the x’s that you would like to use.  You must pick at least three, you may.

Systems. Day 1 Systems of Linear Equations System of Linear Equations: two or more linear equations together The solution of the system of equations.

9.4 – Solving Absolute Value Equations and Inequalities 1.

SYSTEMS OF LINEAR INEQUALITIES

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

Linear Equations Objectives: Find slope Graph Lines

The slope-intercept form of a linear equation of a non-vertical line is given by: Slope-Intercept Form of a Linear Equation.

Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation.

Graph the boundary line the same as if the problem was a linear equation.  Pretend that there is an equal sign and use an appropriate method to graph.

Lines and Slopes.

3.3 Solving Systems of Inequalities by Graphing Pg. 123 Standards addressed: 2.1 & 2.2.

Ch 5.1 Graphing Systems Objective: To solve a system of linear equations by graphing.

Linear Systems of Equations

Warm UP: Solve and check: 1) 3n – 7 = 262) 3(-4x + 2) = 6(2 + x) Solve and graph each solution on a number line: 3) 5p > 10 or -2p ≤ 10 Solve and check:

3.4 Linear Programming p Optimization - Finding the minimum or maximum value of some quantity. Linear programming is a form of optimization where.

© William James Calhoun, 2001 OBJECTIVE: The student will graph inequalities in the coordinate plane. All of the inequalities we have dealt with in this.

Lesson 2.10 Solving Linear Inequalities in Two Variables Concept: Represent and Solve Systems of Inequalities Graphically EQ: How do I represent the solutions.

Algebra 2 Graphing Linear Inequalities in Two Variables.

 1.  2..27v-1.6=.32v-2. Slope-Intercept Form y = mx + b m = slope b = y-intercept Slope-Intercept Form y = mx + b m = slope b = y-intercept.

Graphing Linear Inequalities in Two Variables A linear inequality in two variables takes one of the following forms: The solution of a linear inequality.

9.5 Inequalities and two variables

Lesson 3.3 Systems of Inequalities Objective: To graph linear inequalities, systems of inequalities, and solve linear programming problems.

5.2: Solving Systems of Equations using Substitution

Graphing Linear Equations. Standard Form Equation where x and y are on the same side of the equal sign. Example:

Graphing a Linear Inequality

Chapter 7.5. Graphing Systems of Inequalities Lesson Objective: NCSCOS 2.01 Students will know how to graph a system of linear inequalities.

Warm-up Solve each system of equations:

Bkevil Slope-Intercept Form of a Linear Equation y = mx + b.

9.3 – Linear Equation and Inequalities 1. Linear Equations 2.

Linear Inequalities Page 178. Formulas of Lines Slope Formula Slope Intercept Form Point Slope Form Ax + By = C Standard Form A,B,C ∈ℤ, A ≥ 0 Ax + By.

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

Table of Contents Graphing Linear Inequalities in Two Variables A linear inequality in two variables takes one of the following forms: The solution of.

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

Graphing Linear Inequalities in Two Variables Objective: Graph all of the solutions to a linear inequality.

Name: Date: Topic: Linear Inequalities Essential Question: How can the infinite number of solutions of a linear inequality be represented? Warm-Up: Graph.

3-5: Linear Programming. Learning Target I can solve linear programing problem.

Linear Programming. What is linear programming? Use a system of constraints (inequalities) to find the vertices of the feasible region (overlapping shaded.

3.3 Linear Programming. Vocabulary Constraints: linear inequalities; boundary lines Objective Function: Equation in standard form used to determine the.

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

Solving Systems of Equations Graphing Linear Inequalities.

 An equation of a line can be written in slope- intercept form y = mx + b where m is the slope and b is the y- intercept.  The y-intercept is where.

3.4 Linear Programming p Optimization - Finding the minimum or maximum value of some quantity. Linear programming is a form of optimization where.

Lesson 2.8 Graph Linear Inequalities in Two Variables.

Some Algebra Review By: Mrs. Brown. Functions and Relations Which relation is NOT a function?

Graphing Lines Using Slope Intercept Form Algebra 1 Glencoe McGraw-HillLinda Stamper.

Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation.

Lesson 7.5, page 755 Systems of Inequalities

Solving Systems of Linear Equations and Inequalities by Graphing

Systems of Equations/Inequalities

Linear Inequalities.

3.2 Linear Programming 3 Credits AS

3-3 Optimization with Linear Programming

Linear Programming.

Do Now! Solve the system of equations Do all work on the notecard.

Bellwork Determine whether the ordered pairs are solutions of the inequality: 2x-3y>-2 1.) (0,0) 2.) (0,1)

Systems of Inequalities and Linear Programming

Linear Inequalities.

Graphing a Linear Inequality

LINEARPROGRAMMING 4/26/2019 9:23 AM 4/26/2019 9:23 AM 1.

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 –

1.6 Linear Programming Pg. 30.

Linear Programming.

Chapter 2 Section 7 Two-Variable 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 –

Presentation transcript:

Graph and solve systems of linear inequalitites A-CED 3

Review graphing linear equations Slope-Intercept form 1. Plot a point on the y-axis (y-intercept) 2.Plot the second point by counting the rise and run (slope) from the y-intercept point.

Review graphing linear equations Standard Form 1. Put in slope-intercept form (solve for y).

Review graphing linear equations Vertical Line Horizontal Line

What does a graph represent?  Graphs represent solutions of the equation.

If I wanted to graph an inequality, how would I represent all possible ordered pairs that are solutions to the problem? SSHADE

Graphing Inequalities Graph the line using y-intercept and slope Since the problem is an inequality, we need to shade one side of the line to represent all the possible solutions to the inequality.

If the shaded region represents the solutions to the inequality, how can I check my answer? Pick a point and substitute in the inequality to see if the statement is true.

Graphing Inequalities I pick the origin (0,0) Therefore the shading is correct.

Graphing Inequalities I pick the origin (0,0) Shade the side of the line containing the origin.

Graphing Inequalities NOTE: You can not pick a point that lines on the line. I pick the point (-1,3) Shade the side opposite the point you picked.

Graphing Inequalities

Linear Programming  Your club plans to raise money by selling two sizes of fruit baskets. The plan is to buy small baskets for $10 and sell them for $15 and buy large baskets for $15 and sell them for $24. The club president estimates that you will not sell more than 100 baskets. Your club can afford to spend up to $1200 to buy baskets. Find the number of small and large baskets you should buy in order to maximize profit.

Objective Function: 5x + 9y (maximum profit) x = # of small baskets y = # of large baskets Total baskets constraint Total spending constraint baskets minimum constraint Feasibility region vertices

Objective Function: 5x + 9y (maximum profit) x = # of small baskets y = # of large baskets Feasibility region (0, 80) (60, 40) (0, 0) (100, 0) vertices

Objective Function: 5x + 9y (maximum profit) x = # of small baskets y = # of large baskets (0, 80) (60, 40) (0, 0) (100, 0) minimum maximum Check for maximum profit by plugging each vertice of the feasibility region into the objective function.