Graphical Solutions of Linear Systems
|
|
|
- Adela Bishop
- 5 years ago
- Views:
Transcription
1 Graphical Solutions of Linear Systems Consistent System (At least one solution) Inconsistent System (No Solution) Independent (One solution) Dependent (Infinite many solutions) Parallel Lines Equations are different Equations are the same Slopes are the same 1
2 Solving Systems by Graphing System of Linear Equations two or more linear equations Solving a System of Equations by Graphing STEP 1 Both equations must be in slopeintercept form (y = mx + b) STEP 2 Graph each equation. You need to plot as many points possible to get the most accurate line. STEP 3 Determine the point where the lines intersect. STEP 4 Check the point by substituting into both equations 2
3 Example Solve each system by graphing. y = x + 4 y = x + 2 Example Solve each system by graphing. x + y = 3 x 2y = 0 3
4 Solving Systems of Equations by Substitution Step 1 Solve one equation for one variable Step 2 Substitute for the variable from Step 1 into the other equation. Step 3 Substitute for the variable from Step 2 into any of the original two equations. 4
5 Example Solve each system by substitution. y = 2x x + 2y = 15 5
6 Example Solve each system by substitution. x + y = 3 x = 2y 6
7 Example Solve each system by substitution. 2x = 2y + 6 2x 3y = 6 7
8 Solving Systems of Equations by Elimination Step 1 Align the like terms Step 2 Eliminate one of the variables. Solve for the remaining variable. Step 3 Substitute for the variable from Step 2 into any of the original two equations. 8
9 Example Solve each system by elimination. x + 2y = 9 x + 3y = 16 9
10 Example Solve each system by elimination. 2x + y = 9 3x y = 16 10
11 Example Solve each system by elimination. 3x + 5y = 7 10x + 5y = 0 11
12 Example Solve each system by elimination. 3x + y = 7 2x 2y = 6 12
13 Example Solve each system by elimination. 3x + 2y = 1 4x + 3y = 2 13
14 Graphing Linear Inequalities Linear inequality resembles a linear equation, but with an inequality symbol instead of an equal sign. Step 1 Write your equation in slope intercept form ( y = mx + b). Must follow inequality rules! Step 2 Graph (Use m and b) Step 3 Determine whether your line is dashed or solid. or solid < or > dashed Step 4 Shade appropriate side. > or shade upper part < or shade lower part 14
15 Example Graph the linear inequality y > 3x
16 Example Graph the linear inequality y 2x 3 16
17 Example Graph the linear inequality 3y > 2x
18 Example Graph the linear inequality 5x 2y < 10 18
19 Example Graph the linear inequality x 2y 8 19
20 Example Graph the linear inequality y 2 20
21 Example Graph the linear inequality x > 1 21
22 Systems of Inequalities A set of two or more inequalities. Step 1 Each equation has to be in slope intercept form Step 2 Graph each line. (Use slope and y intercept). Step 3 Determine solid or dashed line and shade appropriate side. 22
23 Example Solve each system of inequalities by graphing. y > 2x + 3 y 3x
24 Example Solve each system of inequalities by graphing. y 3x 6 m = 3 1 b = 6 x + y < 6 x x y < x + 6 m = 1 1 b = 6 24
25 Example Solve each system of inequalities by graphing. 6x + 3y < 6 6x 6x 3y < 6x y < 2x + 2 m = 2 1 b = 2 x + y 2 +x +x y x + 2 m = 1 1 b = 2 25
Put the following equations to slope-intercept form then use 2 points to graph
Tuesday September 23, 2014 Warm-up: Put the following equations to slope-intercept form then use 2 points to graph 1. 4x - 3y = 8 8 x 6y = 16 2. 2x + y = 4 2x + y = 1 Tuesday September 23, 2014 Warm-up:
6-4 Solving Special Systems
6-4 Solving Special Systems Warm Up Lesson Presentation Lesson Quiz 1 2 pts Bell Quiz 6-4 Solve the equation. 1. 2(x + 1) = 2x + 2 3 pts Solve by using any method. 2. y = 3x + 2 2x + y = 7 5 pts possible
Sections 8.1 & 8.2 Systems of Linear Equations in Two Variables
Sections 8.1 & 8.2 Systems of Linear Equations in Two Variables Department of Mathematics Porterville College September 7, 2014 Systems of Linear Equations in Two Variables Learning Objectives: Solve Systems
Graphing Systems of Linear Equations
Graphing Systems of Linear Equations Groups of equations, called systems, serve as a model for a wide variety of applications in science and business. In these notes, we will be concerned only with groups
Consistent and Dependent
Graphing a System of Equations System of Equations: Consists of two equations. The solution to the system is an ordered pair that satisfies both equations. There are three methods to solving a system;
Chapter 1-2 Add and Subtract Integers
Chapter 1-2 Add and Subtract Integers Absolute Value of a number is its distance from zero on the number line. 5 = 5 and 5 = 5 Adding Numbers with the Same Sign: Add the absolute values and use the sign
8 Wyner Honors Algebra II Fall 2013
8 Wyner Honors Algebra II Fall 2013 CHAPTER THREE: SOLVING EQUATIONS AND SYSTEMS Summary Terms Objectives The cornerstone of algebra is solving algebraic equations. This can be done with algebraic techniques,
CHAPTER 5 LINEAR SYSTEMS
CHAPTER 5 LINEAR SYSTEMS Systems of Linear equations have either one solution (independent), no solutions (inconsistent), or infinitely many solutions (dependent). An independent system is the case when
6-4 Solving Special Systems
Warm Up Solve each equation. 1. 2x + 3 = 2x + 4 2. 2(x + 1) = 2x + 2 3. Solve 2y 6x = 10 for y Solve by using any method. 4. y = 3x + 2 2x + y = 7 5. x y = 8 x + y = 4 Know: Solve special systems of linear
To determine the slope or rate of change of a linear function, use m =, positive slopes, rises from left to right, negative
Common Core Regents Review Linear Functions The standard form for a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. To determine the slope or rate of change
Chapter 5: Systems of Equations and Inequalities. Section 5.4. Check Point Exercises
Chapter : Systems of Equations and Inequalities Section. Check Point Eercises. = y y = Solve the first equation for y. y = + Substitute the epression + for y in the second equation and solve for. ( + )
Math-2A Lesson 13-3 (Analyzing Functions, Systems of Equations and Inequalities) Which functions are symmetric about the y-axis?
Math-A Lesson 13-3 (Analyzing Functions, Systems of Equations and Inequalities) Which functions are symmetric about the y-axis? f ( x) x x x x x x 3 3 ( x) x We call functions that are symmetric about
Math 4: Advanced Algebra Ms. Sheppard-Brick A Quiz Review Learning Targets
5A Quiz Review Learning Targets 4.4 5.5 Key Facts Graphing one-variable inequalities (ex. x < 4 ) o Perform algebra steps to get x alone! If you multiply or divide by a negative number, you must flip the
1.5 F15 O Brien. 1.5: Linear Equations and Inequalities
1.5: Linear Equations and Inequalities I. Basic Terminology A. An equation is a statement that two expressions are equal. B. To solve an equation means to find all of the values of the variable that make
You try: What is the equation of the line on the graph below? What is the equation of the line on the graph below?
1 What is the equation of the line on the graph below? 2 3 1a What is the equation of the line on the graph below? y-intercept Solution: To write an equation in slope-intercept form, identify the slope
5 Systems of Equations
Systems of Equations Concepts: Solutions to Systems of Equations-Graphically and Algebraically Solving Systems - Substitution Method Solving Systems - Elimination Method Using -Dimensional Graphs to Approximate
Graphing Linear Systems
Graphing Linear Systems Goal Estimate the solution of a system of linear equations by graphing. VOCABULARY System of linear equations A system of linear equations is two or more linear equations in the
Systems of Equations and Inequalities. College Algebra
Systems of Equations and Inequalities College Algebra System of Linear Equations There are three types of systems of linear equations in two variables, and three types of solutions. 1. An independent system
Solving and Graphing Inequalities
Solving and Graphing Inequalities Graphing Simple Inequalities: x > 3 When finding the solution for an equation we get one answer for x. (There is only one number that satisfies the equation.) For 3x 5
2-7 Solving Quadratic Inequalities. ax 2 + bx + c > 0 (a 0)
Quadratic Inequalities In One Variable LOOKS LIKE a quadratic equation but Doesn t have an equal sign (=) Has an inequality sign (>,
Systems of Linear Equations and Inequalities
Systems of Linear Equations and Inequalities Alex Moore February 4, 017 1 What is a system? Now that we have studied linear equations and linear inequalities, it is time to consider the question, What
Chapter 6. Systems of Equations and Inequalities
Chapter 6 Systems of Equations and Inequalities 6.1 Solve Linear Systems by Graphing I can graph and solve systems of linear equations. CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.A.REI.6 What is a system
SOLVING INEQUALITIES and 9.1.2
SOLVING INEQUALITIES 9.1.1 and 9.1.2 To solve an inequality in one variable, first change it to an equation and solve. Place the solution, called a boundary point, on a number line. This point separates
Due for this week. Slide 2. Copyright 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
MTH 209 Week 1 Due for this week Homework 1 (on MyMathLab via the Materials Link) Monday night at 6pm. Read Chapter 6.1-6.4, 7.1-7.4,10.1-10.3,10.6 Do the MyMathLab Self-Check for week 1. Learning team
Graphing Linear Inequalities
Graphing Linear Inequalities Linear Inequalities in Two Variables: A linear inequality in two variables is an inequality that can be written in the general form Ax + By < C, where A, B, and C are real
STUDY GUIDE FOR TEST 2. Project 3: Fill in the blanks and do the assigned questions. 11/6/07
STUDY GUIDE FOR TEST 2 Name: Project 3: Fill in the blanks and do the assigned questions. 11/6/07 Quadrant II Quadrant I ORDERED PAIR: The first number in the ordered pair is the -coordinate and the second
2.4 Graphing Inequalities
.4 Graphing Inequalities Why We Need This Our applications will have associated limiting values - and either we will have to be at least as big as the value or no larger than the value. Why We Need This
1. Solutions to Systems of Linear Equations. Determine whether the ordered pairs are solutions to the system. x y 6. 3x y 2
78 Chapter Sstems of Linear Equations Section. Concepts. Solutions to Sstems of Linear Equations. Dependent and Inconsistent Sstems of Linear Equations. Solving Sstems of Linear Equations b Graphing Solving
Solving Systems of Linear Equations
Section 2.3 Solving Systems of Linear Equations TERMINOLOGY 2.3 Previously Used: Equivalent Equations Literal Equation Properties of Equations Substitution Principle Prerequisite Terms: Coordinate Axes
Practice Test - Chapter 2
1 State the domain and range of the relation shown in the table Then determine if it is a function If it is a function, determine if it is one-to-one, onto, both, or neither 4 Write 2y = 6x + 4 in standard
Topic: Solving systems of equations with linear and quadratic inequalities
Subject & Grade: Mathematics, 9 th Grade Topic: Solving systems of equations with linear and quadratic inequalities Aim: How would you find the solution set of a linear and quadratic inequality? Materials:.
4.1 Solving Systems of Equations Graphically. Draw pictures to represent the possible number of solutions that a linear-quadratic system can have:
4.1 Solving Systems of Equations Graphically Linear- Quadratic A Linear-Quadratic System of Equations is a linear equation and a quadratic equation involving the same two variables. The solution(s) to
U2Q5 (Module 7 Practice Quiz)
Name: lass: ate: I: U2Q5 (Module 7 Practice Quiz) Multiple hoice Identify the choice that best completes the statement or answers the question. Ï y = x + 8 1. Solve Ô Ì. ÓÔ x + y = 7 a. This system has
Chapter 2 Linear Equations and Inequalities in One Variable
Chapter 2 Linear Equations and Inequalities in One Variable Section 2.1: Linear Equations in One Variable Section 2.3: Solving Formulas Section 2.5: Linear Inequalities in One Variable Section 2.6: Compound
Basic Equations and Inequalities
Hartfield College Algebra (Version 2017a - Thomas Hartfield) Unit ONE Page - 1 - of 45 Topic 0: Definition: Ex. 1 Basic Equations and Inequalities An equation is a statement that the values of two expressions
C. Incorrect! This symbol means greater than or equal to or at least. D. Correct! This symbol means at most or less than or equal to.
SAT Math - Problem Drill 10: Inequalities No. 1 of 10 1. Choose the inequality symbol that means at most. (A) > (B) < (C) (D) (E) This symbol means greater than. This symbol means less than. This symbol
CLEP Precalculus - Problem Drill 15: Systems of Equations and Inequalities
CLEP Precalculus - Problem Drill 15: Systems of Equations and Inequalities No. 1 of 10 1. What are the methods to solve a system of equations? (A) Graphing, replacing, substitution and matrix techniques.
Section 1.6. Functions
Section 1.6 Functions Definitions Relation, Domain, Range, and Function The table describes a relationship between the variables x and y. This relationship is also described graphically. x y 3 2 4 1 5
Sample: Do Not Reproduce LF6 STUDENT PAGES LINEAR FUNCTIONS STUDENT PACKET 6: SYSTEMS OF LINEAR EQUATIONS. Name Period Date
Name Period Date LINEAR FUNCTIONS STUDENT PACKET 6: SYSTEMS OF LINEAR EQUATIONS LF6.1 LF6.2 LF6.3 Introduction to Systems of Linear Equations Understand the definition of a system of linear equations Understand
Chapter 1 Linear Equations and Graphs
Chapter 1 Linear Equations and Graphs Section R Linear Equations and Inequalities Important Terms, Symbols, Concepts 1.1. Linear Equations and Inequalities A first degree, or linear, equation in one variable
OBJECTIVES UNIT 1. Lesson 1.0
OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint
Name Class Date. What is the solution to the system? Solve by graphing. Check. x + y = 4. You have a second point (4, 0), which is the x-intercept.
6-1 Reteaching Graphing is useful for solving a system of equations. Graph both equations and look for a point of intersection, which is the solution of that system. If there is no point of intersection,
Intro Activity 1.1 Translate verbal expressions into algebraic expressions with three or fewer terms
First Quarter ** NOTE: Include SOL review throughout each quarter. Stress application problems throughout the year. A good resource for fractions is on pp. 914-915. Review of prerequisite skills can be
MAFS Algebra 1. Systems of Equations and Inequalities. Day 10 - Student Packet
MAFS Algebra 1 Systems of Equations and Inequalities Day 10 - Student Packet Day 10: Systems of Equations and Inequalities MAFS.912.A-REI.3.5, MAFS.912.A-REI.3.6, MAFS.912.A-REI.4.10 I CAN graph a system
Algebra I Assessment. Eligible Texas Essential Knowledge and Skills
Algebra I Assessment Eligible Texas Essential Knowledge and Skills STAAR Algebra I Assessment Reporting Category 1: Functional Relationships The student will describe functional relationships in a variety
Section 3.4 Writing the Equation of a Line
Chapter Linear Equations and Functions Section.4 Writing the Equation of a Line Writing Equations of Lines Critical to a thorough understanding of linear equations and functions is the ability to write
Chapter 6: Systems of Equations and Inequalities
Chapter 6: Sstems of Equations and Inequalities 6-1: Solving Sstems b Graphing Objectives: Identif solutions of sstems of linear equation in two variables. Solve sstems of linear equation in two variables
SKILL BUILDER TEN. Graphs of Linear Equations with Two Variables. If x = 2 then y = = = 7 and (2, 7) is a solution.
SKILL BUILDER TEN Graphs of Linear Equations with Two Variables A first degree equation is called a linear equation, since its graph is a straight line. In a linear equation, each term is a constant or
Lesson 28: Another Computational Method of Solving a Linear System
Lesson 28: Another Computational Method of Solving a Linear System Student Outcomes Students learn the elimination method for solving a system of linear equations. Students use properties of rational numbers
Solving Equations Quick Reference
Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number
CHAPTER 1: Graphs, Functions, and Models
CHAPTER 1: Graphs, Functions, and Models 1.1 Introduction to Graphing 1.2 Functions and Graphs 1.3 Linear Functions, Slope, and Applications 1.4 Equations of Lines and Modeling 1.5 Linear Equations, Functions,
Number of (Nested) Shopping Carts Three nested shopping carts are shown.
Randy must fit shopping carts into an area that has a length of 82 feet and a width of one shopping cart. He made some measurements necessary for his computations. The table shows the length of a set of
Unit 6. Systems of Linear Equations. 3 weeks
Unit 6 Systems of Linear Equations 3 weeks Unit Content Investigation 1: Solving Systems of Linear Equations (3 days) Investigation 2: Solving Systems of Linear Equations by Substitution (4 days) Investigation
Systems of Linear Equations with the System Solver
Systems of Linear Equations with the System Solver In these activities, you explore the steps involved in solving systems of linear equations. You ll make observations about the effects of those operations
Math 1 Unit 1 EOC Review
Math 1 Unit 1 EOC Review Name: Solving Equations (including Literal Equations) - Get the variable to show what it equals to satisfy the equation or inequality - Steps (each step only where necessary):
Solving Linear and Rational Inequalities Algebraically. Definition 22.1 Two inequalities are equivalent if they have the same solution set.
Inequalities Concepts: Equivalent Inequalities Solving Linear and Rational Inequalities Algebraically Approximating Solutions to Inequalities Graphically (Section 4.4).1 Equivalent Inequalities Definition.1
Characteristics of Linear Functions (pp. 1 of 8)
Characteristics of Linear Functions (pp. 1 of 8) Algebra 2 Parent Function Table Linear Parent Function: x y y = Domain: Range: What patterns do you observe in the table and graph of the linear parent
Algebra I Keystone Quiz Linear Inequalities - (A ) Systems Of Inequalities, (A ) Interpret Solutions To Inequality Systems
Algebra I Keystone Quiz Linear Inequalities - (A1.1.3.2.1) Systems Of Inequalities, (A1.1.3.2.2) Interpret Solutions To Inequality Systems 1) Student Name: Teacher Name: Jared George Date: Score: The linear
PLC Papers Created For:
PLC Papers Created For: Josh Angles and linear graphs Graphs of Linear Functions 1 Grade 4 Objective: Recognise, sketch and interpret graphs of linear functions. Question 1 Sketch the graph of each function,
Quadratic and Polynomial Inequalities in one variable have look like the example below.
Section 8 4: Polynomial Inequalities in One Variable Quadratic and Polynomial Inequalities in one variable have look like the example below. x 2 5x 6 0 (x 2) (x + 4) > 0 x 2 (x 3) > 0 (x 2) 2 (x + 4) 0
2 Which graph shows the solution to the following
1 In order for Josh to graph the solution to the inequality 4x 2y > 6, which of the following steps does he need to use? Select all that apply. A. Shade above the line. B. Draw the line y = 2x 3 as a solid
Name Period Date Ch. 5 Systems of Linear Equations Review Guide
Reteaching 5-1 Solving Systems by Graphing ** A system of equations is a set of two or more equations that have the same variables. ** The solution of a system is an ordered pair that satisfies all equations
USING THE QUADRATIC FORMULA and 9.1.3
Chapter 9 USING THE QUADRATIC FORMULA 9.1.2 and 9.1.3 When a quadratic equation is not factorable, another method is needed to solve for x. The Quadratic Formula can be used to calculate the roots of a
A. Incorrect! Replacing is not a method for solving systems of equations.
ACT Math and Science - Problem Drill 20: Systems of Equations No. 1 of 10 1. What methods were presented to solve systems of equations? (A) Graphing, replacing, and substitution. (B) Solving, replacing,
6-6 Solving Systems of Linear Inequalities 6-6. Solving Systems of Linear Inequalities
6-6 Solving Systems of Linear Inequalities Warm Up Lesson Presentation Lesson Quiz 1 2 pts 3 pts 5 pts Bell Quiz 6-6 Solve each inequality for y. 1. 8x + y < 6 2. 3x 2y > 10 3. Graph the solutions of 4x
y z ). Write all solutions using only positive
1. a) Graph the equation x y =. b) What is the x-intercept? What is the y-intercept? d) What is the slope of this line?. a) Find the slope of the line joining the points and ( b) Find the equation of this
Secondary I Chapter 7 Practice Test
.. Secondar I Chapter 7 Practice Test. The graph of which inequalit would be represented with a dashed line? a. b. c. d. Graph the sstem of linear inequalities. 7 x 7 7 x 7. Graph the solution to this
SCIE 4101 Spring Math Review Packet #2 Notes Algebra I
SCIE 4101 Spring 011 Math Review Packet # Notes Algebra I I consider Algebra and algebraic thought to be the heart of mathematics everything else before that is arithmetic. The first characteristic of
Chapter 6. Functions. 01/2017 LSowatsky 1
Chapter 6 Functions 01/2017 LSowatsky 1 6.1A Constant Rate of Change I can Identify proportional and nonproportional linear relationships by finding a constant rate of change CCSS 8.EE.5, 8.F.4 LSowatsky
Math 0312 Intermediate Algebra Chapter 1 and 2 Test Review
Math 0312 Intermediate Algebra Chapter 1 and 2 Test Review Name Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation for y. 1)
6-1 Using Graphs to Solve a System of Equations., together form a system of linear equations.
AH Notes# 6-1 Using Graphs to Solve a System of Equations Two or more linear equations in the same variables, such as, together form a system of linear equations. The solution to the system is any/all
MATH 115: Review for Chapter 6
MATH 115: Review for Chapter 6 In order to prepare for our test on Chapter 6, ou need to understand and be able to work problems involving the following topics: I SYSTEMS OF LINEAR EQUATIONS CONTAINING
OREGON STANDARDS MAP. (Algebra I)
OREGON STANDARDS MAP (Algebra I) R.01 R.02 R.03 AR.01 AR.02 Language ALGEBRA I Primary Citations Supporting Citations Represent, analyze and determine 1.17 to 1.18 1.21 to 1.22 rules for finding patterns
Prentice Hall Mathematics, Course
Prentice Hall Mathematics, Course 3 2010 Grade 8 C O R R E L A T E D T O North Carolina s, Mathematics Grade 8 (Adopted 2009) North Carolina s, Mathematics Math 8 (Adopted 2009) North Carolina s Mathematics
HMH Fuse Algebra correlated to the. Texas Essential Knowledge and Skills for Mathematics High School Algebra 1
HMH Fuse Algebra 1 2012 correlated to the Texas Essential Knowledge and Skills for Mathematics High School Algebra 1 111.32. Algebra I (b) Knowledge and skills. (1) Foundations for functions. The student
Module 2 Study Guide. The second module covers the following sections of the textbook: , 4.1, 4.2, 4.5, and
Module 2 Study Guide The second module covers the following sections of the textbook: 3.3-3.7, 4.1, 4.2, 4.5, and 5.1-5.3 Sections 3.3-3.6 This is a continuation of the study of linear functions that we
C.3 Nonlinear Systems of Equations and Inequalities
50 section C3 C.3 Nonlinear Systems of Equations and Inequalities In section E, we discussed methods of solving systems of two linear equations. Recall that solutions to such systems are the intercepts
MAT116 Final Review Session Chapter 1: Equations, Inequalities, and Modeling
MAT116 Final Review Session Chapter 1: Equations, Inequalities, and Modeling Solving Equations: Types of Equations in Chapter 1: Linear Absolute Value Quadratic Rational To SOLVE an equation means to find
SCIE 4101 Fall Math Review Packet #2 Notes Patterns and Algebra I Topics
SCIE 4101 Fall 014 Math Review Packet # Notes Patterns and Algebra I Topics I consider Algebra and algebraic thought to be the heart of mathematics everything else before that is arithmetic. The first
Department of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections 3.1, 3.3, and 3.5
Department of Mathematics, University of Wisconsin-Madison Math 11 Worksheet Sections 3.1, 3.3, and 3.5 1. For f(x) = 5x + (a) Determine the slope and the y-intercept. f(x) = 5x + is of the form y = mx
College Algebra Through Problem Solving (2018 Edition)
City University of New York (CUNY) CUNY Academic Works Open Educational Resources Queensborough Community College Winter 1-25-2018 College Algebra Through Problem Solving (2018 Edition) Danielle Cifone
Algebra 1 Prince William County Schools Pacing Guide (Crosswalk)
Algebra 1 Prince William County Schools Pacing Guide 2017-2018 (Crosswalk) Teacher focus groups have assigned a given number of days to each unit based on their experiences and knowledge of the curriculum.
Algebra I Calculator Activities
First Nine Weeks SOL Objectives Calculating Measures of Central Tendency SOL A.17 Organize a set of data Calculate the mean, median, mode, and range of a set of data Describe the relationships between
Note: Two perpendicular lines form a system of the first type. (Nothing special about being )
Math 100 Elementary Algebra Sec 7.1: Solving Linear Systems by Graphing Two or more equations [inequalities] in several variables that are considered simultaneously are called a system of equations [inequalities].
Pair of Linear Equations in Two Variables
Pair of Linear Equations in Two Variables Linear equation in two variables x and y is of the form ax + by + c= 0, where a, b, and c are real numbers, such that both a and b are not zero. Example: 6x +
Minnesota K-12 Academic Standards in Mathematics (2007)
8.1.1.1 Classify real numbers as rational or irrational. Know that when a square root of a positive integer is not an integer, then it is irrational. Know that the sum of a rational number an irrational
8. Find r a! r b. a) r a = [3, 2, 7], r b = [ 1, 4, 5] b) r a = [ 5, 6, 7], r b = [2, 7, 4]
![8. Find r a! r b. a) r a = [3, 2, 7], r b = [ 1, 4, 5] b) r a = [ 5, 6, 7], r b = [2, 7, 4]](/thumbs/95/122742655.jpg "8. Find r a! r b. a) r a = [3, 2, 7], r b = [ 1, 4, 5] b) r a = [ 5, 6, 7], r b = [2, 7, 4]")
Chapter 8 Prerequisite Skills BLM 8-1.. Linear Relations 1. Make a table of values and graph each linear function a) y = 2x b) y = x + 5 c) 2x + 6y = 12 d) x + 7y = 21 2. Find the x- and y-intercepts of
Order of Operations. Real numbers
Order of Operations When simplifying algebraic expressions we use the following order: 1. Perform operations within a parenthesis. 2. Evaluate exponents. 3. Multiply and divide from left to right. 4. Add
3 RD 9 WEEKS. EE 1 EE 3 EE 4 EE 7a EE 7b EE 8a EE 8b EE 8c SP 1 SP 2 SP 3 SP 4 F 2 F 3 F 5
1ST 9 WEEKS 2ND 9 WEEKS 3 RD 9 WEEKS 4 TH 9 WEEKS NS 1 NS 2 EE 2 G 1 G 2 G 3 G 4 G 5 EE 1 G 9 G 6 G 7 G 8 G 5 EE 5 EE 6 F 1 F 2 EE 1 EE 3 EE 4 EE 7a EE 7b EE 8a EE 8b EE 8c SP 1 SP 2 SP 3 SP 4 SP 4 SP
Section 1.4. Meaning of Slope for Equations, Graphs, and Tables
Section 1.4 Meaning of Slope for Equations, Graphs, and Tables Finding Slope from a Linear Equation Finding Slope from a Linear Equation Example Find the slope of the line Solution Create a table using
14.1 Systems of Linear Equations in Two Variables
86 Chapter 1 Sstems of Equations and Matrices 1.1 Sstems of Linear Equations in Two Variables Use the method of substitution to solve sstems of equations in two variables. Use the method of elimination
6.5 Systems of Inequalities
6.5 Systems of Inequalities Linear Inequalities in Two Variables: A linear inequality in two variables is an inequality that can be written in the general form Ax + By < C, where A, B, and C are real numbers
Question 1. Find the coordinates of the y-intercept for. f) None of the above. Question 2. Find the slope of the line:
of 4 4/4/017 8:44 AM Question 1 Find the coordinates of the y-intercept for. Question Find the slope of the line: of 4 4/4/017 8:44 AM Question 3 Solve the following equation for x : Question 4 Paul has
CK-12 Middle School Math Grade 8
CK-12 Middle School Math aligned with COMMON CORE MATH STATE STANDARDS INITIATIVE Middle School Standards for Math Content Common Core Math Standards for CK-12 Middle School Math The Number System (8.NS)
Herndon High School Geometry Honors Summer Assignment
Welcome to Geometry! This summer packet is for all students enrolled in Geometry Honors at Herndon High School for Fall 07. The packet contains prerequisite skills that you will need to be successful in
Section 2.7 Notes Name: Date: Polynomial and Rational Inequalities
Section.7 Notes Name: Date: Precalculus Polynomial and Rational Inequalities At the beginning of this unit we solved quadratic inequalities by using an analysis of the graph of the parabola combined with
Algebra Non-Calculator Skills Inventory Solutions
Algebra Non-Calculator Skills Inventory Solutions 1. True or False: If a and b are non-zero real numbers then = + a + b a b Solution: False. Example: If a = 4 and b = 1, then = + 5 4 + 1 4 1 b + a The
FOR ALL STUDENTS TAKING ALGEBRA II Honors SUMMER REVIEW PACKET
FOR ALL STUDENTS TAKING ALGEBRA II Honors 01-014 SUMMER REVIEW PACKET Dear Student and Parent/Guardian, The math department at Central Dauphin School District wants you to be successful in Algebra II.
Example #1: Write an Equation Given Slope and a Point Write an equation in slope-intercept form for the line that has a slope of through (5, - 2).
Algebra II: 2-4 Writing Linear Equations Date: Forms of Equations Consider the following graph. The line passes through and. Notice that is the y-intercept of. You can use these two points to find the
MA 1128: Lecture 08 03/02/2018. Linear Equations from Graphs And Linear Inequalities
MA 1128: Lecture 08 03/02/2018 Linear Equations from Graphs And Linear Inequalities Linear Equations from Graphs Given a line, we would like to be able to come up with an equation for it. I ll go over