# Packet: Lines (Part 1) Standards covered:

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Packet: Lines (Part 1) Standards covered: *(2)MA.912.A.3.8 Graph a line given any of the following information: a table of values, the x and y- intercepts, two points, the slope and a point, the equation of the line in slope- intercept form, standard form, or point- slope form. (Also assesses MA.912.A.3.12.) *(4)MA.912.A.3.9 Determine the slope, x- intercept, and y- intercept of a line given its graph, its equation, or two points on the line. (Also assesses MA.912.A.3.12.) *MA.912.A.3.12 Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. (Assessed with MA.912.A.3.8, MA.912.A.3.9, MA.912.A.3.10, and MA.912.A.3.11.) Section 5 Lines (Part 1) 1

2 Section 5 Video 1 Lines, the Great Unknown Lets say you work the night shift, and make \$11/hour. If you happened to get called in a night you are not working, you get \$50 for just coming in. Hours worked: x Money Earned: Section 5 Lines (Part 1) 2

3 If you weigh 200 lbs and want to lose some weight You go on a diet and start losing, on average, 3lbs each week. Weeks on a diet: x Your weight: Important Equations Slope formula (on your reference sheet): slope = m =!!!!!!!!!! Forms of equations: Point Slope (on reference sheet): y y! = m x x! (for Standard Form) Slope Intercept (on reference sheet): y = mx + b Standard Form: Ax + By = C Section 5 Lines (Part 1) 3

4 Section 5 Video 2 Find Slope from a Graph, 2 Points, or an Equation Let s think about slope. Slope measures a graph s speed. Positive slope Negative Slope Zero Slope Study Edge Tip If you are not sure if the slope of a line is positive or negative, draw 2 vertical lines on each side. Ø If the graph makes the letter N, it has a Negative slope. Ø If the graph does not make the letter N, it has a positive slope. If you see two points on a graph, we call this method rise over run. slope = rise run Section 5 Lines (Part 1) 4

5 Try it! Section 5 Lines (Part 1) 5

6 Ø Slope formula (on your reference sheet): slope = m =!!!!!!!!!! Ø If you are given 2 points, label them (x!, y! ) and (x!, y! ), then plug in! Find the slope between the points (2, 5) and (- 3, 7) Try it! Find the slope between the points (- 3, 8) and (5, - 2) Section 5 Lines (Part 1) 6

7 Ø Find the slope of the line with the following equation: y = mx + b Ø If you have an equation, solve the equation for y. The coefficient of x will be the slope. y = 3x + 4 y + 7 = 2x Try it! y = 4 3 x + 3 2x + 3y = 4 Section 5 Lines (Part 1) 7

8 BEAT THE TEST! 1. Two points on a given path are (10,25) and (5,20). Find the slope of the path. Section 5 Lines (Part 1) 8

9 2. In a game, Ender needed to travel along the path 3x 4y = 10 in order to avoid his opponent. What was the slope of his course? A.!! B.!! C.!! D.!! Section 5 Lines (Part 1) 9

10 3. Enrique flew his model airplane with a slope of!. Which of the! following graphs could have been the flight path? A. C. B. D. Section 5 Lines (Part 1) 10

11 Section 5 Video 3 Find Intercepts from a Graph, 2 Points, Equation There are three different cases that we need to be able to find intercepts: 1. A Graph 2. An Equation 3. Two points 1. If you have a graph, just look where the line hits the x- axis and y- axis! Ø x- intercept o Where the line hits the x- axis (and y = 0) o Will be in the form (x, 0) Ø y- intercept o Where the line hits the y- axis (and x = 0) o Will be in the form (0,y) On the graph to the right, find the intercepts. x- int: y- int: Section 5 Lines (Part 1) 11

12 2. If you have an equation, Ø To find the y intercept, replace a 0 for x and solve for y Ø To find the x intercept, replace a 0 for y and solve for x Find the x and y intercepts: 2x + 5y = 10 Try it! Find the x and y intercepts: y = 3x + 2 Section 5 Lines (Part 1) 12

13 3. If you are given 2 points, we are going to use a couple of equations off your equation sheet!!! Ø First, find the slope: slope = m =!!!!!!!!!! Ø Use Point Slope form: y y! = m x x! Let s try the points (3, 2) and (1, - 1). Find the two intercepts. Try it! (4, - 2), (- 5, 3) Section 5 Lines (Part 1) 13

14 BEAT THE TEST! 1. A plane is currently at 200 ft and is descending at 10 feet per minute. The path of the gliding plane can be given by the following equation, y = 10x where y is the height of the plane and x is the number of minutes. In how many minutes will the plane land? (Hint: In other words, what is the x- intercept?) A. 10 B. 20 C. 100 D. 200 Section 5 Lines (Part 1) 14

15 2. What is the coordinate of the y intercept of the following graph? Round to the nearest integer. Section 5 Lines (Part 1) 15

16 3. Given the following equation, Find the x- intercept. 2x + 5y = A graph goes through the points (1,1) and (- 5,5). What is the y- intercept? Section 5 Lines (Part 1) 16

17 Section 5 Video 4 Make a Graph from Points and/or Slope Ø Plot the two points and draw a line through them. Draw a line through the points (1,5) and (4,- 3) Ø Sometimes you are given a point and a slope Suppose a line goes through the point (2,1) and has a slope of!! 1. P the point you know 2. Use the slope to draw another point, using slope = rise run 3. Draw a line through the two points Section 5 Lines (Part 1) 17

18 BEAT THE TEST! 1. A line has an x intercept of 3 and a slope of!. Which graph! represents the line? A. C. B. D. Section 5 Lines (Part 1) 18

19 2. A surveyor s line goes through a special set of coordinates at (- 2,4) and (2,- 1) Which of the following could be the graph? A. C. B. D. Section 5 Lines (Part 1) 19

20 Section 5 Video 5 Identify a Graph from an Equation If you have an equation, you can identify the graph a couple of ways Ø We will be focused on drawing lines here, and later you will be identifying lines Intercepts Method Ø Replace x with 0 and solve for y. That s the y intercept! Ø Replace y with 0 and solve for x. That s the x intercept! Ø Plot the intercepts and draw a line through them 2x 3y = 6 Section 5 Lines (Part 1) 20

21 Try it! 8x = 12 4y Slope Intercept Method y = mx + b 1. Solve the equation for y. 2. The y intercept is b, plot that point. 3. The slope is m, use rise over run to plot the second point. y = 2x + 1 Section 5 Lines (Part 1) 21

22 Try it! x + y = 1 Section 5 Lines (Part 1) 22

23 BEAT THE TEST! 1. Which is the graph of the following equation? 2x 5y = 10 A. C. B. D. Section 5 Lines (Part 1) 23

24 2. Which of the following graph could represent the equation below? y = 35x A. C. B. D. Section 5 Lines (Part 1) 24

25 Section 5 Lines (Part 1) 25

### Section 1.4 Notes Page Linear Equations in Two Variables and Linear Functions., x

Section. Notes Page. Linear Equations in Two Variables and Linear Functions Slope Formula The slope formula is used to find the slope between two points ( x, y ) and ( ) x, y. x, y ) The slope is the vertical

### 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

### 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

### 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

### 9.1 Solving Quadratic Equations by Finding Square Roots Objectives 1. Evaluate and approximate square roots.

9.1 Solving Quadratic Equations by Finding Square Roots 1. Evaluate and approximate square roots. 2. Solve a quadratic equation by finding square roots. Key Terms Square Root Radicand Perfect Squares Irrational

### 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

### 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

### Lines and Linear Equations. Slopes

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

### What students need to know for... ALGEBRA II

What students need to know for... ALGEBRA II 2015-2016 NAME Students expecting to take Algebra II at Cambridge Rindge & Latin School should demonstrate the ability to... General: o Keep an organized notebook

### Equations of Lines Derivations

Equations of Lines Derivations If you know how slope is defined mathematically, then deriving equations of lines is relatively simple. We will start off with the equation for slope, normally designated

### 2.7. The straight line. Introduction. Prerequisites. Learning Outcomes. Learning Style

The straight line 2.7 Introduction Probably the most important function and graph that you will use are those associated with the straight line. A large number of relationships between engineering variables

### 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

### 5.1: Rate of Change and Slope

5.1: Rate of Change and Slope Rate of Change shows relationship between changing quantities. On a graph, when we compare rise and run, we are talking about steepness of a line (slope). You can use and

Review Session #5 Quadratics Discriminant How can you determine the number and nature of the roots without solving the quadratic equation? 1. Prepare the quadratic equation for solving in other words,

### 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

### Section 3.2. Graphing linear equations

Section 3.2 Graphing linear equations Learning objectives Graph a linear equation by finding and plotting ordered pair solutions Graph a linear equation and use the equation to make predictions Vocabulary:

### Solving Quadratic Equations by Completing the Square

9. Solving Quadratic Equations by Completing the Square 9. OBJECTIVES 1. Solve a quadratic equation by the square root method. Solve a quadratic equation by completing the square. Solve a geometric application

Quadratic Modeling Business 10 Profits In this activity, we are going to look at modeling business profits. We will allow q to represent the number of items manufactured and assume that all items that

### MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem. Constant Rate of Change/Slope

MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem Constant Rate of Change/Slope In a Table Relationships that have straight-lined graphs

### 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

### In this section, we ll review plotting points, slope of a line and different forms of an equation of a line.

Math 1313 Section 1.2: Straight Lines In this section, we ll review plotting points, slope of a line and different forms of an equation of a line. Graphing Points and Regions Here s the coordinate plane:

### 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

### 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

### Chapter 8 Graphs and Functions:

Chapter 8 Graphs and Functions: Cartesian axes, coordinates and points 8.1 Pictorially we plot points and graphs in a plane (flat space) using a set of Cartesian axes traditionally called the x and y axes

### with "a", "b" and "c" representing real numbers, and "a" is not equal to zero.

3.1 SOLVING QUADRATIC EQUATIONS: * A QUADRATIC is a polynomial whose highest exponent is. * The "standard form" of a quadratic equation is: ax + bx + c = 0 with "a", "b" and "c" representing real numbers,

Definition of the Quadratic Formula The Quadratic Formula uses the a, b and c from numbers; they are the "numerical coefficients"., where a, b and c are just The Quadratic Formula is: For ax 2 + bx + c

### Packet: Systems of Equations

Packet: Systems of Equations Standards covered: *MA.912.A.3.13 Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology. (Assessed

### Ordered Pairs. Graphing Lines and Linear Inequalities, Solving System of Linear Equations. Cartesian Coordinates System.

Ordered Pairs Graphing Lines and Linear Inequalities, Solving System of Linear Equations Peter Lo All equations in two variables, such as y = mx + c, is satisfied only if we find a value of x and a value

### 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

### Section 3.4 The Slope Intercept Form: y = mx + b

Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept Reminding! m = y x = y 2 y 1 x 2 x 1 Slope of a horizontal line is 0 Slope of a vertical line is Undefined Graph a linear

### The Slope-Intercept Form

7.1 The Slope-Intercept Form 7.1 OBJECTIVES 1. Find the slope and intercept from the equation of a line. Given the slope and intercept, write the equation of a line. Use the slope and intercept to graph

### 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

### 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

### Many different kinds of animals can change their form to help them avoid or

Slopes, Forms, Graphs, and Intercepts Connecting the Standard Form with the Slope-Intercept Form of Linear Functions Learning Goals In this lesson, you will: Graph linear functions in standard form. Transform

9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation

### Pre-AP Algebra 2 Unit 3 Lesson 1 Quadratic Functions

Unit 3 Lesson 1 Quadratic Functions Objectives: The students will be able to Identify and sketch the quadratic parent function Identify characteristics including vertex, axis of symmetry, x-intercept,

### graphs, Equations, and inequalities

graphs, Equations, and inequalities You might think that New York or Los Angeles or Chicago has the busiest airport in the U.S., but actually it s Hartsfield-Jackson Airport in Atlanta, Georgia. In 010,

### Session 3 Solving Linear and Quadratic Equations and Absolute Value Equations

Session 3 Solving Linear and Quadratic Equations and Absolute Value Equations 1 Solving Equations An equation is a statement expressing the equality of two mathematical expressions. It may have numeric

### Helpsheet. Giblin Eunson Library LINEAR EQUATIONS. library.unimelb.edu.au/libraries/bee. Use this sheet to help you:

Helpsheet Giblin Eunson Library LINEAR EQUATIONS Use this sheet to help you: Solve linear equations containing one unknown Recognize a linear function, and identify its slope and intercept parameters Recognize

### Algebra 1 Chapter 3 Vocabulary. equivalent - Equations with the same solutions as the original equation are called.

Chapter 3 Vocabulary equivalent - Equations with the same solutions as the original equation are called. formula - An algebraic equation that relates two or more real-life quantities. unit rate - A rate

### Linear Equations and Graphs

2.1-2.4 Linear Equations and Graphs Coordinate Plane Quadrants - The x-axis and y-axis form 4 "areas" known as quadrants. 1. I - The first quadrant has positive x and positive y points. 2. II - The second

### 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

### 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,,

### Writing Prompts Intermediate Algebra. M. E. Waggoner, Simpson College Indianola, Iowa Updated March 30, 2016

Writing Prompts Intermediate Algebra M. E. Waggoner, Simpson College Indianola, Iowa Updated March 30, 2016 Contents Chapter 1: Real Numbers and Expressions... 3 Chapter 2: Linear Equations and Inequalities...

### REVIEW SHEETS INTERMEDIATE ALGEBRA MATH 95

REVIEW SHEETS INTERMEDIATE ALGEBRA MATH 95 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts which are taught in the specified math course. The sheets

### 4.1 & Linear Equations in Slope-Intercept Form

4.1 & 4.2 - Linear Equations in Slope-Intercept Form Slope-Intercept Form: y = mx + b Ex 1: Write the equation of a line with a slope of -2 and a y-intercept of 5. Ex 2:Write an equation of the line shown

### Lesson 36 MA 152, Section 3.1

Lesson 36 MA 5, Section 3. I Quadratic Functions A quadratic function of the form y = f ( x) = ax + bx + c, where a, b, and c are real numbers (general form) has the shape of a parabola when graphed. The

### Pre-AP Algebra 2 Lesson 2-5 Graphing linear inequalities & systems of inequalities

Lesson 2-5 Graphing linear inequalities & systems of inequalities Objectives: The students will be able to - graph linear functions in slope-intercept and standard form, as well as vertical and horizontal

### Study Resources For Algebra I. Unit 1D Systems of Equations and Inequalities

Study Resources For Algebra I Unit 1D Systems of Equations and Inequalities This unit explores systems of linear functions and the various methods used to determine the solution for the system. Information

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:

### MAT12X Intermediate Algebra

MAT1X Intermediate Algebra Workshop I Quadratic Functions LEARNING CENTER Overview Workshop I Quadratic Functions General Form Domain and Range Some of the effects of the leading coefficient a The vertex

### ALGEBRA I (Common Core)

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, August 13, 2014 8:30 a.m. MODEL RESPONSE SET Table of Contents Question 25...................

### 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

### Name: Date: Block: Midterm Exam Review Sheet 1

Name: Date: Block: Midterm Exam Review Sheet 1 Chapter 1 1. Write a variable expression for 2. Simplify: 8 3 2 4 seven divided by the sum of x and five 3. Write an algebraic expression for 4. Write an

### Exam 2 Review. 3. How to tell if an equation is linear? An equation is linear if it can be written, through simplification, in the form.

Exam 2 Review Chapter 1 Section1 Do You Know: 1. What does it mean to solve an equation? To solve an equation is to find the solution set, that is, to find the set of all elements in the domain of the

### For any two different places on the number line, the integer on the right is greater than the integer on the left.

Positive and Negative Integers Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5,.... Negative integers are all the opposites of these whole numbers: -1, -2, -3, -4, -5,. We

### Name: Class: Date: Does the equation represent a direct variation? If so, find the constant of variation. c. yes; k = 5 3. c.

Name: Class: Date: Chapter 5 Test Multiple Choice Identify the choice that best completes the statement or answers the question. What is the slope of the line that passes through the pair of points? 1.

### Homework #1 Solutions

Homework #1 Solutions Problems Section 1.1: 8, 10, 12, 14, 16 Section 1.2: 2, 8, 10, 12, 16, 24, 26 Extra Problems #1 and #2 1.1.8. Find f (5) if f (x) = 10x x 2. Solution: Setting x = 5, f (5) = 10(5)

### Beginning of the Semester To-Do List

Beginning of the Semester To-Do List Set up your account at https://casa.uh.edu/ Read the Math 13xx Departmental Course Policies Take Course Policies Quiz until your score is 100%. You can find it on the

### Math 150: Summer 2011 Test 3, Form: A

Math 150: Summer 2011 Test 3, Form: A Name: Read all of the following information before starting the exam: It is to your advantage to answer ALL of the questions. There are 15 multiple choice and 5 short

### Pre-Calculus III Linear Functions and Quadratic Functions

Linear Functions.. 1 Finding Slope...1 Slope Intercept 1 Point Slope Form.1 Parallel Lines.. Line Parallel to a Given Line.. Perpendicular Lines. Line Perpendicular to a Given Line 3 Quadratic Equations.3

### CHAPTER 2: POLYNOMIAL AND RATIONAL FUNCTIONS

CHAPTER 2: POLYNOMIAL AND RATIONAL FUNCTIONS 2.01 SECTION 2.1: QUADRATIC FUNCTIONS (AND PARABOLAS) PART A: BASICS If a, b, and c are real numbers, then the graph of f x = ax2 + bx + c is a parabola, provided

### Polynomial and Rational Functions

Polynomial and Rational Functions Quadratic Functions Overview of Objectives, students should be able to: 1. Recognize the characteristics of parabolas. 2. Find the intercepts a. x intercepts by solving

### Systems of Linear Equations in Two Variables

Chapter 6 Systems of Linear Equations in Two Variables Up to this point, when solving equations, we have always solved one equation for an answer. However, in the previous chapter, we saw that the equation

### Homework #5 Solutions

Homework # Solutions Problems Bolded problems are worth 2 points. Section 2.3: 10, 16, 26 Section 2.4: 2, 6, 10, 22, 28 Section 3.1: 4, 14, 24, 28, 36, 38, 0, 60 2.3.10. On May 9, 2007, CBS Evening News

### PLOTTING DATA AND INTERPRETING GRAPHS

PLOTTING DATA AND INTERPRETING GRAPHS Fundamentals of Graphing One of the most important sets of skills in science and mathematics is the ability to construct graphs and to interpret the information they

### 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

### 5-1. Lesson Objective. Lesson Presentation Lesson Review

5-1 Using Transformations to Graph Quadratic Functions Lesson Objective Transform quadratic functions. Describe the effects of changes in the coefficients of y = a(x h) 2 + k. Lesson Presentation Lesson

### Linear Equations Review

Linear Equations Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The y-intercept of the line y = 4x 7 is a. 7 c. 4 b. 4 d. 7 2. What is the y-intercept

### 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

Graphing Quadratic Functions In our consideration of polynomial functions, we first studied linear functions. Now we will consider polynomial functions of order or degree (i.e., the highest power of x

### 3.1. Quadratic Equations and Models. Quadratic Equations Graphing Techniques Completing the Square The Vertex Formula Quadratic Models

3.1 Quadratic Equations and Models Quadratic Equations Graphing Techniques Completing the Square The Vertex Formula Quadratic Models 3.1-1 Polynomial Function A polynomial function of degree n, where n

Assessment Coordinate System and Slope Helpful Formula Pitch = Rise / Run Grade = Rise / Run M = (Y Y 1 ) / (X X 1 ); X= Run, Y= Rise, C=Grade Length X + Y = C X = C - Y X = C Y Round your answer to the

### Final Graphing Practice #1

Final Graphing Practice #1 Beginning Algebra / Math 100 Fall 2013 506 (Prof. Miller) Student Name/ID: Instructor Note: Assignment: Set up a tutoring appointment with one of the campus tutors or with me.

### The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value, or {y y 8}.

Use a table of values to graph each equation. State the domain and range. 1. y = 2x 2 + 4x 6 x y = 2x 2 + 4x 6 (x, y) 3 y = 2( 3) 2 + 4( 3) 6 = 0 ( 3,0) 2 y = 2( 2) 2 + 4( 2) 6 = ( 2, 6) 6 1 y = 2( 1)

### MA107 Precalculus Algebra Exam 2 Review Solutions

MA107 Precalculus Algebra Exam 2 Review Solutions February 24, 2008 1. The following demand equation models the number of units sold, x, of a product as a function of price, p. x = 4p + 200 a. Please write

### 3.3. Solving Polynomial Equations. Introduction. Prerequisites. Learning Outcomes

Solving Polynomial Equations 3.3 Introduction Linear and quadratic equations, dealt within Sections 3.1 and 3.2, are members of a class of equations, called polynomial equations. These have the general

### Chapter 2. Looking at Data: Relationships. Introduction to the Practice of STATISTICS SEVENTH. Moore / McCabe / Craig. Lecture Presentation Slides

Chapter 2 Looking at Data: Relationships Introduction to the Practice of STATISTICS SEVENTH EDITION Moore / McCabe / Craig Lecture Presentation Slides Chapter 2 Looking at Data: Relationships 2.1 Scatterplots

### SCATTER PLOTS AND TREND LINES

Name SCATTER PLOTS AND TREND LINES VERSION 2 Lessons 1 3 1. You have collected the following data while researching the Winter Olympics. You are trying to determine if there is a relationship between the

### CHAPTER 3: REPRESENTATIONS OF A LINE (4 WEEKS)...

Table of Contents CHAPTER : REPRESENTATIONS OF A LINE (4 WEEKS)... SECTION.0 ANCHOR PROBLEM: SOLUTIONS TO A LINEAR EQUATION... 6 SECTION.1: GRAPH AND WRITE EQUATIONS OF LINES... 8.1a Class Activity: Write

MA 134 Lecture Notes August 20, 2012 Introduction The purpose of this lecture is to... Introduction The purpose of this lecture is to... Learn about different types of equations Introduction The purpose

### 4.1 Graph Quadratic Functions in Standard Form (Parabolas) Tuesday, June 08, 2010

4.1 Graph Quadratic Functions in Standard Form (Parabolas) Tuesday, June 08, 2010 12:31 PM Vertex Axis of symmetry Link to Parabola Animation Another Cool Animation Ch 4 Page 1 Graph: Graph: Graph: 3.

### TIME VALUE OF MONEY PROBLEM #8: NET PRESENT VALUE Professor Peter Harris Mathematics by Sharon Petrushka

TIME VALUE OF MONEY PROBLEM #8: NET PRESENT VALUE Professor Peter Harris Mathematics by Sharon Petrushka Introduction Creativity Unlimited Corporation is contemplating buying a machine for \$100,000, which

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

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

### D. ( 1 5 )2. Grade 8 Mathematics Item Specifications Florida Standards Assessments. MAFS.8.EE.1 Work with radicals and integer exponents.

MAFS.8.EE.1 Work with radicals and integer exponents. MAFS.8.EE.1.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 2 3 5 = 3 3 = 1 3 2 =

### 7-1 Graphing Exponential Functions. Graph each function. State the domain and range. x

Graph each function. State the domain and range. 1. f () = 2 Domain = {all real numbers}; Range = {f () f () > 0} 2. f () = 5 Page 1 Domain = {all real numbers}; 7-1 Graphing Range = {feponential () f

### Title: Graphing Quadratic Equations in Standard Form Class: Math 100 or 107 Author: Sharareh Masooman Instructions to tutor: Read instructions under

Title: Graphing Quadratic Equations in Standard Form Class: Math 100 or 107 Author: Sharareh Masooman Instructions to tutor: Read instructions under Activity and follow all steps for each problem exactly

### P210 Graphing Problem Solving Lab

P210 Graphing Problem Solving Lab Objective: Learn how to present different types of data using graphs, both manually and using Microsoft Excel 7.0 Step one is to manually graph each of the following using

### Answer on Question #48173 Math Algebra

Answer on Question #48173 Math Algebra On graph paper, draw the axes, and the lines y = 12 and x = 6. The rectangle bounded by the axes and these two lines is a pool table with pockets in the four corners.

### Ways We Use Integers. Negative Numbers in Bar Graphs

Ways We Use Integers Problem Solving: Negative Numbers in Bar Graphs Ways We Use Integers When do we use negative integers? We use negative integers in several different ways. Most of the time, they are

### Experiment 4 Analysis by Gas Chromatography

Experiment 4 Analysis by Gas Chromatography In this experiment we will study the method of gas chromatography. Gas chromatography (GC) is one of the most important analytical tools that the chemist has.

### How can you write an equation of a line when you are given the slope and the y-intercept of the line? ACTIVITY: Writing Equations of Lines

. Writing Equations in Slope-Intercept Form How can ou write an equation of a line when ou are given the slope and the -intercept of the line? ACTIVITY: Writing Equations of Lines Work with a partner.

### Scatterplots. Section 3.1 Scatterplots & Correlation. Scatterplots. Explanatory & Response Variables. Scatterplots and Correlation

Section 3.1 Scatterplots & Correlation Scatterplots A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal

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

### The Parabola and the Circle

The Parabola and the Circle The following are several terms and definitions to aid in the understanding of parabolas. 1.) Parabola - A parabola is the set of all points (h, k) that are equidistant from

### 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