# Creating Equations. Set 3: Writing Linear Equations Instruction. Student Activities Overview and Answer Key

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Creating Equations Instruction Goal: To provide opportunities for students to develop concepts and skills related to writing linear equations in slope-intercept and standard form given two points and a point and slope Common Core Standards Algebra: Creating Equations Create equations that describe numbers or relationships. A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Algebra: Reasoning with Equations and Inequalities Represent and solve equations and inequalities graphically. A-REI.0. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Student Activities Overview and Answer Key Station Students will be given spaghetti noodles, graph paper, and the general point-slope form of an equation. Students will use the spaghetti noodles to model different equations. Then they will write the slope-intercept form of an equation given the slope and y-intercept. They will also write the slopeintercept form of an equation given the y-intercept and a parallel or perpendicular equation. Answers. y = 5x y = 4x 8 3. y = x y = 4x Walch Education Algebra I Station Activities for Common Core Standards

2 Creating Equations Station 2 Instruction Students will be given spaghetti noodles, graph paper, and the general slope-intercept and pointslope forms of a linear equation. They will determine which form of the equation to use first in order to write a linear equation when given the slope and a point on the line. They will use spaghetti noodles to model the equations. Then they will write the slope-intercept form of a line given the slope and a point on the line. Answers. Use point-slope form first because you can plug in the given point for x and y. 2. y = 2x y = x y = 3x y = 2 x Station 3 Students will be given a number cube. They will use it to populate two ordered pairs. From the ordered pairs, they will find the slope and write the equation in slope-intercept form. Then they will explain how they found the slope and the equation in slope-intercept form. Answers. Answers will vary. 2. Answers will vary. 3. Answers will vary. 4. Slope = rise run = y2 y x2 x 5. Find the slope from the two points. Plug one of the points and the slope into y = mx + b to find b. Then write the equation in slope-intercept form. 00 Algebra I Station Activities for Common Core Standards 20 Walch Education

3 Creating Equations Station 4 Students will be given 0 index cards with the following equations written on them: Instruction y = 2x + 2 y = 5x 8 y = x + 6 y = 2 x 20 y = 0x x + 2y = 32 2x + 3y = 60 4x 2y = 24 5x + y = 36 x y = They will work as a group to match the equations written in standard form with the equations written in slope-intercept form. Then they convert an equation written in standard form to slopeintercept form and vice versa. Answers. y = x + 6and x + 2y = y = 2 x 20and2x + 3y = y = 0x 24 and 5x + y = x 2y = 24 and y = 2x x y = 4 andy = 5x y = x x 5y = 50 Materials List/Setup Station Station 2 Station 3 Station 4 spaghetti noodles; graph paper spaghetti noodles; graph paper number cube 0 index cards with the following equations written on them: y = 2x + 2 y = 5x 8 y = x + 6 y = 2 x 20 y = 0x x + 2y = 32 2x + 3y = 60 4x 2y = 24 5x + y = 36 x y = Walch Education Algebra I Station Activities for Common Core Standards

4 Creating Equations Discussion Guide Instruction To support students in reflecting on the activities and to gather some formative information about student learning, use the following prompts to facilitate a class discussion to debrief the station activities. Prompts/Questions. How do you write the standard form of a linear equation? 2. How do you write the slope-intercept form of a linear equation? 3. How do you write the slope-intercept form of a linear equation given a point and the slope? 4. How do you write the slope-intercept form of a linear equation given two points on the line? 5. How do you convert the standard form of a linear equation into slope-intercept form? 6. How do you convert the slope-intercept form of a linear equation into standard form? Think, Pair, Share Have students jot down their own responses to questions, then discuss with a partner (who was not in their station group), and then discuss as a whole class. Suggested Appropriate Responses. ax + by = c 2. y = mx + b 3. Use the point-slope form of the equation to plug in the given point and slope. Then write the equation in slope-intercept form. 4. Find the slope from the two points. Plug one of the points and the slope into y = mx + b to find b. Then write the equation in slope-intercept form. 5. Solve for y. 6. Move the x-value to the left-hand side of the equation by using either the addition or subtraction property of equality and make sure that the coefficients are whole numbers with the coefficient of x being positive. Possible Misunderstandings/Mistakes Mixing up the x- and y-values when plugging them into the point-slope or slope-intercept forms Not keeping track of positive and negative signs when converting from standard form to slope-intercept form and vice versa Incorrectly finding the slope as run rise 02 Algebra I Station Activities for Common Core Standards instead of rise run 20 Walch Education

5 NAME: Creating Equations Station You will find spaghetti noodles and graph paper at this station. Draw a coordinate plane on your graph paper by creating and labeling the x-axis and the y-axis. For each problem, use the given information and the spaghetti to find the slope-intercept form of the equation. Slope-intercept form is written as y = mx + b.. The equation has a y-intercept of (0, 0) and a slope of 5. Model this equation using the spaghetti. Then write the equation in slope-intercept form. 2. The equation has a y-intercept of (0, 8) and is parallel to the line y = 4x 6. Model this equation using the spaghetti. Then write the equation in slope-intercept form. 3. The equation has a y-intercept of 8 and is perpendicular to the line y = 3x + 9. Model this equation using the spaghetti. Then write the equation in slope-intercept form. 4. The graph of the equation passes through the origin and is perpendicular to y x 4. Model this equation using the spaghetti. Then write the equation in slope-intercept form Walch Education Algebra I Station Activities for Common Core Standards

6 NAME: Creating Equations Station 2 You will find spaghetti noodles and graph paper at this station. Draw a coordinate plane on your graph paper by creating and labeling the x-axis and the y-axis. Use the spaghetti and what you know about the slope-intercept and point-slope forms of a linear equation to answer the questions. Slope-intercept form is written as y = mx + b. Point-slope form is written as y y = m(x x ).. You want to find a linear equation. Which form should you use first if you are given the slope and a point on the line? 2. Use spaghetti to model a line that has a slope of 2 and passes through ( 3, 8). Then write the equation for this line in slope-intercept form. 3. Use spaghetti to model a line that has a slope of equation for this line in slope-intercept form. 8 and passes through (, 2). Then write the 4. Use spaghetti to model a line that has a slope of 3 and passes through ( 4, 0). Then write the equation for this line in slope-intercept form. 5. Use spaghetti to model a line that has a slope of 2 the equation for this line in slope-intercept form. 5 and passes through ( 5, 20). Then write 04 Algebra I Station Activities for Common Core Standards 20 Walch Education

7 NAME: Creating Equations Station 3 You will be given a number cube. For each problem, roll the number cube four times to create two ordered pairs. Then use these ordered pairs to find the slope and write the equation in slopeintercept form. Slope-intercept form is written as y = mx + b.. First ordered pair: (, ) Second ordered pair: (, ) Slope = Equation written in slope-intercept form: 2. First ordered pair: (, ) Second ordered pair: (, ) Slope = Equation written in slope-intercept form: 3. First ordered pair: (, ) Second ordered pair: (, ) Slope = Equation written in slope-intercept form: 4. How did you find the slope from the two ordered pairs? 5. How did you find b in the slope-intercept form of the equation? Walch Education Algebra I Station Activities for Common Core Standards

8 NAME: Creating Equations Station 4 At this station, you will find 0 index cards with the following equations written on them: y = 2x + 2 y = 5x 8 y = x + 6 y = 2 x 20 y = 0x x + 2y = 32 2x + 3y = 60 4x 2y = 24 5x + y = 36 x y = As a group, shuffle the cards. Work as a group to match the linear equation written in standard form with the same equation written in slope-intercept form. Write your matches on the lines below Rewrite the equation 3x + 9y = 2 so that it s in slope-intercept form. Show your work. 7. Rewrite the equation y = x 0 so that it s in standard form. Show your work Algebra I Station Activities for Common Core Standards 20 Walch Education

### Reasoning with Equations and Inequalities

Instruction Goal: To provide opportunities for students to develop concepts and skills related to solving quadratic equations using the square root property. The quadratic equations will have two solutions,

### Warm Up. Write an equation given the slope and y-intercept. Write an equation of the line shown.

Warm Up Write an equation given the slope and y-intercept Write an equation of the line shown. EXAMPLE 1 Write an equation given the slope and y-intercept From the graph, you can see that the slope is

### Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}

Linear Equations Domain and Range Domain refers to the set of possible values of the x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in

### A synonym is a word that has the same or almost the same definition of

Slope-Intercept Form Determining the Rate of Change and y-intercept Learning Goals In this lesson, you will: Graph lines using the slope and y-intercept. Calculate the y-intercept of a line when given

### Slope-Intercept Equation. Example

1.4 Equations of Lines and Modeling Find the slope and the y intercept of a line given the equation y = mx + b, or f(x) = mx + b. Graph a linear equation using the slope and the y-intercept. Determine

### Reasoning with Equations and Inequalities

Instruction Goal: To provide opportunities for students to develop concepts and skills related to solving linear sstems of equations b graphing Common Core Standards Algebra: Solve sstems of equations.

### Section 1.4 Graphs of Linear Inequalities

Section 1.4 Graphs of Linear Inequalities A Linear Inequality and its Graph A linear inequality has the same form as a linear equation, except that the equal symbol is replaced with any one of,,

### Write the Equation of the Line Review

Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Objective: Students will be assessed on their ability to write the equation of a line in multiple methods. Connections

### Section 1.1 Linear Equations: Slope and Equations of Lines

Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of

### What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.

PRIMARY CONTENT MODULE Algebra - Linear Equations & Inequalities T-37/H-37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of

1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points

### Answer Key Building Polynomial Functions

Answer Key Building Polynomial Functions 1. What is the equation of the linear function shown to the right? 2. How did you find it? y = ( 2/3)x + 2 or an equivalent form. Answers will vary. For example,

### Section summaries. d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2. 1 + y 2. x1 + x 2

Chapter 2 Graphs Section summaries Section 2.1 The Distance and Midpoint Formulas You need to know the distance formula d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 and the midpoint formula ( x1 + x 2, y ) 1 + y 2

### Graphing Linear Equations

Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope

### Solving Equations Involving Parallel and Perpendicular Lines Examples

Solving Equations Involving Parallel and Perpendicular Lines Examples. The graphs of y = x, y = x, and y = x + are lines that have the same slope. They are parallel lines. Definition of Parallel Lines

### EQUATIONS and INEQUALITIES

EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line

### GRAPHING LINEAR EQUATIONS IN TWO VARIABLES

GRAPHING LINEAR EQUATIONS IN TWO VARIABLES The graphs of linear equations in two variables are straight lines. Linear equations may be written in several forms: Slope-Intercept Form: y = mx+ b In an equation

### Sect The Slope-Intercept Form

Concepts # and # Sect. - The Slope-Intercept Form Slope-Intercept Form of a line Recall the following definition from the beginning of the chapter: Let a, b, and c be real numbers where a and b are not

### What are the place values to the left of the decimal point and their associated powers of ten?

The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything

### Coordinate Plane, Slope, and Lines Long-Term Memory Review Review 1

Review. What does slope of a line mean?. How do you find the slope of a line? 4. Plot and label the points A (3, ) and B (, ). a. From point B to point A, by how much does the y-value change? b. From point

### The Point-Slope Form

7. The Point-Slope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope

### Vocabulary Words and Definitions for Algebra

Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

### Slope-Intercept Form of a Linear Equation Examples

Slope-Intercept Form of a Linear Equation Examples. In the figure at the right, AB passes through points A(0, b) and B(x, y). Notice that b is the y-intercept of AB. Suppose you want to find an equation

### Writing the Equation of a Line in Slope-Intercept Form

Writing the Equation of a Line in Slope-Intercept Form Slope-Intercept Form y = mx + b Example 1: Give the equation of the line in slope-intercept form a. With y-intercept (0, 2) and slope -9 b. Passing

### Chapter 1 Linear Equations and Graphs

Chapter 1 Linear Equations and Graphs Section 1.1 - Linear Equations and Inequalities Objectives: The student will be able to solve linear equations. The student will be able to solve linear inequalities.

### Algebra 1 Chapter 05 Review

Class: Date: Algebra 1 Chapter 05 Review Multiple Choice Identify the choice that best completes the statement or answers the question. Find the slope of the line that passes through the pair of points.

### Set 4: Special Congruent Triangles Instruction

Instruction Goal: To provide opportunities for students to develop concepts and skills related to proving right, isosceles, and equilateral triangles congruent using real-world problems Common Core Standards

### Section 1.10 Lines. The Slope of a Line

Section 1.10 Lines The Slope of a Line EXAMPLE: Find the slope of the line that passes through the points P(2,1) and Q(8,5). = 5 1 8 2 = 4 6 = 2 1 EXAMPLE: Find the slope of the line that passes through

### Math 113 Review for Exam I

Math 113 Review for Exam I Section 1.1 Cartesian Coordinate System, Slope, & Equation of a Line (1.) Rectangular or Cartesian Coordinate System You should be able to label the quadrants in the rectangular

### x x y y Then, my slope is =. Notice, if we use the slope formula, we ll get the same thing: m =

Slope and Lines The slope of a line is a ratio that measures the incline of the line. As a result, the smaller the incline, the closer the slope is to zero and the steeper the incline, the farther the

### CHAPTER 1 Linear Equations

CHAPTER 1 Linear Equations 1.1. Lines The rectangular coordinate system is also called the Cartesian plane. It is formed by two real number lines, the horizontal axis or x-axis, and the vertical axis or

### Chapter 6 Notes. Section 6.1 Solving One-Step Linear Inequalities

Chapter 6 Notes Name Section 6.1 Solving One-Step Linear Inequalities Graph of a linear Inequality- the set of all points on a number line that represent all solutions of the inequality > or < or circle

### 2.3 Writing Equations of Lines

. Writing Equations of Lines In this section ou will learn to use point-slope form to write an equation of a line use slope-intercept form to write an equation of a line graph linear equations using the

### WARM UP EXERCSE. 1-3 Linear Functions & Straight lines

WARM UP EXERCSE A company makes and sells inline skates. The price-demand function is p (x) = 190 0.013(x 10) 2. Describe how the graph of function p can be obtained from one of the library functions.

### PRIMARY CONTENT MODULE Algebra I -Linear Equations & Inequalities T-71. Applications. F = mc + b.

PRIMARY CONTENT MODULE Algebra I -Linear Equations & Inequalities T-71 Applications The formula y = mx + b sometimes appears with different symbols. For example, instead of x, we could use the letter C.

### Lesson 9: Graphing Standard Form Equations Lesson 2 of 2. Example 1

Lesson 9: Graphing Standard Form Equations Lesson 2 of 2 Method 2: Rewriting the equation in slope intercept form Use the same strategies that were used for solving equations: 1. 2. Your goal is to solve

### HIBBING COMMUNITY COLLEGE COURSE OUTLINE

HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE: - Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,

### Example SECTION 13-1. X-AXIS - the horizontal number line. Y-AXIS - the vertical number line ORIGIN - the point where the x-axis and y-axis cross

CHAPTER 13 SECTION 13-1 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants X-AXIS - the horizontal

### Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.

Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear

### Unit 4: Analyze and Graph Linear Equations, Functions, and Relations

Unit 4 Table of Contents Unit 4: Analyze and Graph Linear Equations, Functions and Relations Video Overview Learning Objectives 4.2 Media Run Times 4.3 Instructor Notes 4.4 The Mathematics of Analyzing

### Practice Problems for Exam 1 Math 140A, Summer 2014, July 2

Practice Problems for Exam 1 Math 140A, Summer 2014, July 2 Name: INSTRUCTIONS: These problems are for PRACTICE. For the practice exam, you may use your book, consult your classmates, and use any other

### Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan

Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan I. Topic: Slope-Intercept Form II. III. Goals and Objectives: A. The student will write an equation of a line given information about its graph.

### Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:

### Intro to Linear Equations Algebra 6.0

Intro to Linear Equations Algebra 6.0 Linear Equations: y x 7 y x 5 x y Linear Equations generally contain two variables: x and y. In a linear equation, y is called the dependent variable and x is the

### Algebra Cheat Sheets

Sheets Algebra Cheat Sheets provide you with a tool for teaching your students note-taking, problem-solving, and organizational skills in the context of algebra lessons. These sheets teach the concepts

### IV. ALGEBRAIC CONCEPTS

IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other

### Florida Algebra 1 End-of-Course Assessment Item Bank, Polk County School District

Benchmark: MA.912.A.2.3; Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Also assesses MA.912.A.2.13; Solve

### Building Polynomial Functions

Building Polynomial Functions NAME 1. What is the equation of the linear function shown to the right? 2. How did you find it? 3. The slope y-intercept form of a linear function is y = mx + b. If you ve

### Linear Approximations ACADEMIC RESOURCE CENTER

Linear Approximations ACADEMIC RESOURCE CENTER Table of Contents Linear Function Linear Function or Not Real World Uses for Linear Equations Why Do We Use Linear Equations? Estimation with Linear Approximations

### Practice Test - Chapter 4. y = 2x 3. The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept.

y = 2x 3. The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept. Plot the y-intercept (0, 3). The slope is. From (0, 3), move up 2 units and right 1 unit. Plot

### I. Model Problems. II. Practice III. Challenge Problems VI. Answer Key

www.mathworksheetsgo.com On Twitter: twitter.com/mathprintables I. Model Problems. II. Practice III. Challenge Problems VI. Answer Key Web Resources Equations of Lines www.mathwarehouse.com/algebra/linear_equation/equation-of-a-line-formula.php

### LINEAR FUNCTIONS. Form Equation Note Standard Ax + By = C A and B are not 0. A > 0

LINEAR FUNCTIONS As previousl described, a linear equation can be defined as an equation in which the highest eponent of the equation variable is one. A linear function is a function of the form f ( )

### Chapter 4.1 Parallel Lines and Planes

Chapter 4.1 Parallel Lines and Planes Expand on our definition of parallel lines Introduce the idea of parallel planes. What do we recall about parallel lines? In geometry, we have to be concerned about

### Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

Task Model 3 Equation/Numeric DOK Level 1 algebraically, example, have no solution because 6. 3. The student estimates solutions by graphing systems of two linear equations in two variables. Prompt Features:

### Section 2.1 Intercepts; Symmetry; Graphing Key Equations

Intercepts: An intercept is the point at which a graph crosses or touches the coordinate axes. x intercept is 1. The point where the line crosses (or intercepts) the x-axis. 2. The x-coordinate of a point

### Graphing - Parallel and Perpendicular Lines

. Graphing - Parallel and Perpendicular Lines Objective: Identify the equation of a line given a parallel or perpendicular line. There is an interesting connection between the slope of lines that are parallel

### 1. Graphing Linear Inequalities

Notation. CHAPTER 4 Linear Programming 1. Graphing Linear Inequalities x apple y means x is less than or equal to y. x y means x is greater than or equal to y. x < y means x is less than y. x > y means

### Algebra 1. Curriculum Map

Algebra 1 Curriculum Map Table of Contents Unit 1: Expressions and Unit 2: Linear Unit 3: Representing Linear Unit 4: Linear Inequalities Unit 5: Systems of Linear Unit 6: Polynomials Unit 7: Factoring

### MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

### Unit 5: Coordinate Geometry Practice Test

Unit 5: Coordinate Geometry Practice Test Math 10 Common Name: Block: Please initial this box to indicate you carefully read over your test and checked your work for simple mistakes. What I can do in this

### Temperature Scales. The metric system that we are now using includes a unit that is specific for the representation of measured temperatures.

Temperature Scales INTRODUCTION The metric system that we are now using includes a unit that is specific for the representation of measured temperatures. The unit of temperature in the metric system is

### 3-4 Equations of Lines

3-4 Equations of Lines Write an equation in slope-intercept form of the line having the given slope and y-intercept. Then graph the 1.m: 4, y-intercept: 3 2. y-intercept: 1 The slope-intercept form of

### Section 1.8 Coordinate Geometry

Section 1.8 Coordinate Geometry The Coordinate Plane Just as points on a line can be identified with real numbers to form the coordinate line, points in a plane can be identified with ordered pairs of

### 1 Functions, Graphs and Limits

1 Functions, Graphs and Limits 1.1 The Cartesian Plane In this course we will be dealing a lot with the Cartesian plane (also called the xy-plane), so this section should serve as a review of it and its

### GRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points?

GRAPHING (2 weeks) The Rectangular Coordinate System 1. Plot ordered pairs of numbers on the rectangular coordinate system 2. Graph paired data to create a scatter diagram 1. How do you graph points? 2.

### Norwalk La Mirada Unified School District. Algebra Scope and Sequence of Instruction

1 Algebra Scope and Sequence of Instruction Instructional Suggestions: Instructional strategies at this level should include connections back to prior learning activities from K-7. Students must demonstrate

### Module: Graphing Linear Equations_(10.1 10.5)

Module: Graphing Linear Equations_(10.1 10.5) Graph Linear Equations; Find the equation of a line. Plot ordered pairs on How is the Graph paper Definition of: The ability to the Rectangular Rectangular

### Example 1. Rise 4. Run 6. 2 3 Our Solution

. Graphing - Slope Objective: Find the slope of a line given a graph or two points. As we graph lines, we will want to be able to identify different properties of the lines we graph. One of the most important

### Solving Systems of Linear Equations Graphing

Solving Systems of Linear Equations Graphing Outcome (learning objective) Students will accurately solve a system of equations by graphing. Student/Class Goal Students thinking about continuing their academic

### 1 You Try. 2 You Try.

1 Simplify. 1 You Try. 1) Simplify. AF 1.2 2 Evaluate if, and. 2 You Try. 2) Evaluate if. 1.0 Page 1 of 19 MDC@ACOE (AUSD) 09/13/10 3 Simplify. 3 You Try. 3) Simplify. NS 1.2 4 Simplify. 4 You Try. 4)

### Lesson Plan Mine Shaft Grade 8 Slope

CCSSM: Grade 8 DOMAIN: Expressions and Equations Cluster: Understand the connections between proportional relationships, lines, and linear equations. Standard: 8.EE.5: Graph proportional relationships,

### Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20

Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding

### Algebra Chapter 6 Notes Systems of Equations and Inequalities. Lesson 6.1 Solve Linear Systems by Graphing System of linear equations:

Algebra Chapter 6 Notes Systems of Equations and Inequalities Lesson 6.1 Solve Linear Systems by Graphing System of linear equations: Solution of a system of linear equations: Consistent independent system:

### Pacing for a Common Core Curriculum with Prentice Hall Algebra 1

Pacing for a Common Core Curriculum with Prentice Hall Algebra 1 This leveled Pacing Guide can help you transition to a Common Core-based curriculum with Pearson s Prentice Hall Algebra 1 2011. The first

### Vector Notation: AB represents the vector from point A to point B on a graph. The vector can be computed by B A.

1 Linear Transformations Prepared by: Robin Michelle King A transformation of an object is a change in position or dimension (or both) of the object. The resulting object after the transformation is called

### Mathematics Placement

Mathematics Placement The ACT COMPASS math test is a self-adaptive test, which potentially tests students within four different levels of math including pre-algebra, algebra, college algebra, and trigonometry.

1.6 A LIBRARY OF PARENT FUNCTIONS Copyright Cengage Learning. All rights reserved. What You Should Learn Identify and graph linear and squaring functions. Identify and graph cubic, square root, and reciprocal

### Solving Systems of Two Equations Algebraically

8 MODULE 3. EQUATIONS 3b Solving Systems of Two Equations Algebraically Solving Systems by Substitution In this section we introduce an algebraic technique for solving systems of two equations in two unknowns

### 2.1 Equations of Lines

Section 2.1 Equations of Lines 1 2.1 Equations of Lines The Slope-Intercept Form Recall the formula for the slope of a line. Let s assume that the dependent variable is and the independent variable is

### 2. Simplify. College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses

College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key 1. Multiply 2 3 5 1 Use the distributive property to remove the parentheses 2 3 5 1 2 25 21 3 35 31 2 10 2 3 15 3 2 13 2 15 3 2

### Equations of Lines and Planes

Calculus 3 Lia Vas Equations of Lines and Planes Planes. A plane is uniquely determined by a point in it and a vector perpendicular to it. An equation of the plane passing the point (x 0, y 0, z 0 ) perpendicular

### Overview. Observations. Activities. Chapter 3: Linear Functions Linear Functions: Slope-Intercept Form

Name Date Linear Functions: Slope-Intercept Form Student Worksheet Overview The Overview introduces the topics covered in Observations and Activities. Scroll through the Overview using " (! to review,

### 5. Equations of Lines: slope intercept & point slope

5. Equations of Lines: slope intercept & point slope Slope of the line m rise run Slope-Intercept Form m + b m is slope; b is -intercept Point-Slope Form m( + or m( Slope of parallel lines m m (slopes

### Solving Systems of Equations with Absolute Value, Polynomials, and Inequalities

Solving Systems of Equations with Absolute Value, Polynomials, and Inequalities Solving systems of equations with inequalities When solving systems of linear equations, we are looking for the ordered pair

### Understanding Basic Calculus

Understanding Basic Calculus S.K. Chung Dedicated to all the people who have helped me in my life. i Preface This book is a revised and expanded version of the lecture notes for Basic Calculus and other

### Congruence. Set 5: Bisectors, Medians, and Altitudes Instruction. Student Activities Overview and Answer Key

Instruction Goal: To provide opportunities for students to develop concepts and skills related to identifying and constructing angle bisectors, perpendicular bisectors, medians, altitudes, incenters, circumcenters,

### The slope m of the line passes through the points (x 1,y 1 ) and (x 2,y 2 ) e) (1, 3) and (4, 6) = 1 2. f) (3, 6) and (1, 6) m= 6 6

Lines and Linear Equations Slopes Consider walking on a line from left to right. The slope of a line is a measure of its steepness. A positive slope rises and a negative slope falls. A slope of zero means

### ModuMath Algebra Lessons

ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations

### Algebra 2 PreAP. Name Period

Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for completing

### Higher Education Math Placement

Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

### Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year.

Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year. Goal The goal of the summer math program is to help students

### Lesson 4: Solving and Graphing Linear Equations

Lesson 4: Solving and Graphing Linear Equations Selected Content Standards Benchmarks Addressed: A-2-M Modeling and developing methods for solving equations and inequalities (e.g., using charts, graphs,

### Make sure you look at the reminders or examples before each set of problems to jog your memory! Solve

Name Date Make sure you look at the reminders or examples before each set of problems to jog your memory! I. Solving Linear Equations 1. Eliminate parentheses. Combine like terms 3. Eliminate terms by

### Algebra I Station Activities for Common Core State Standards

Algebra I Station Activities for Common Core State Standards WALCH EDUCATION The classroom teacher may reproduce materials in this book for classroom use only. The reproduction of any part for an entire

### https://williamshartunionca.springboardonline.org/ebook/book/27e8f1b87a1c4555a1212b...

of 19 9/2/2014 12:09 PM Answers Teacher Copy Plan Pacing: 1 class period Chunking the Lesson Example A #1 Example B Example C #2 Check Your Understanding Lesson Practice Teach Bell-Ringer Activity Students

### MSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions

MSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions The goal of this workshop is to familiarize you with similarities and differences in both the graphing and expression of polynomial

### Algebra II End of Course Exam Answer Key Segment I. Scientific Calculator Only

Algebra II End of Course Exam Answer Key Segment I Scientific Calculator Only Question 1 Reporting Category: Algebraic Concepts & Procedures Common Core Standard: A-APR.3: Identify zeros of polynomials

### The Cartesian Plane The Cartesian Plane. Performance Criteria 3. Pre-Test 5. Coordinates 7. Graphs of linear functions 9. The gradient of a line 13

6 The Cartesian Plane The Cartesian Plane Performance Criteria 3 Pre-Test 5 Coordinates 7 Graphs of linear functions 9 The gradient of a line 13 Linear equations 19 Empirical Data 24 Lines of best fit

Problem 1 The Parabola Examine the data in L 1 and L to the right. Let L 1 be the x- value and L be the y-values for a graph. 1. How are the x and y-values related? What pattern do you see? To enter the