How can you construct and interpret a scatter plot? ACTIVITY: Constructing a Scatter Plot

Size: px
Start display at page:

Download "How can you construct and interpret a scatter plot? ACTIVITY: Constructing a Scatter Plot"

Transcription

1 9. Scatter Plots How can ou construct and interpret a scatter plot? ACTIVITY: Constructing a Scatter Plot Work with a partner. The weights (in ounces) and circumferences C (in inches) of several sports balls are shown. Basketball Soccer Baseball Tennis oz 9 in. 2 oz 3 in. Golf 2 oz 8 in..6 oz.3 in. 6 oz 28 in. Water Polo Softball Racquetball.4 oz 7 in. 7 oz 2 in. oz 27 in. In this lesson, ou will construct and interpret scatter plots. describe patterns in scatter plots. b. Write the weight and circumference C of each ball as an ordered pair. Then plot the ordered pairs in the coordinate plane. c. Describe the relationship between weight and circumference. Are an of the points close together? d. In general, do ou think ou can describe this relationship as positive or negative? linear or nonlinear? Eplain. oz 26 in. C Circumference (inches) a. Choose a scale for the horizontal ais and the vertical ais of the coordinate plane shown. Data Analsis Volleball V Weight (ounces) e. A bowling ball has a weight of 22 ounces and a circumference of 27 inches. Describe the location of the ordered pair that represents this data point in the coordinate plane. How does this point compare to the others? Eplain our reasoning. 372 Chapter 9 ms_blue pe_9.indd 372 Data Analsis and Displas 2/2/ 4:24:3 PM

2 2 ACTIVITY: Constructing a Scatter Plot Math Practice Recognize Usefulness of Tools How do ou know when a scatter plot is a useful tool for making a prediction? Work with a partner. The table shows the number of absences and the final grade for each student in a sample. a. Write the ordered pairs from the table. Then plot them in a coordinate plane. b. Describe the relationship between absences and final grade. How is this relationship similar to the relationship between weight and circumference in Activit? How is it different? c. MODELING A student has been absent 6 das. Use the data to predict the student s final grade. Eplain how ou found our answer. Absences Final Grade ACTIVITY: Identifing Scatter Plots Work with a partner. Match the data sets with the most appropriate scatter plot. Eplain our reasoning. a. month of birth and birth weight for infants at a da care b. quiz score and test score of each student in a class c. age and value of laptop computers i. ii. iii. 4. How would ou define the term scatter plot?. IN YOUR OWN WORDS How can ou construct and interpret a scatter plot? Use what ou learned about scatter plots to complete Eercise 7 on page 376. Section 9. Scatter Plots 373

3 9. Lesson Lesson Tutorials Ke Vocabular scatter plot, p. 374 Scatter Plot A scatter plot is a graph that shows the relationship between two data sets. The two sets of data are graphed as ordered pairs in a coordinate plane. EXAMPLE Interpreting a Scatter Plot Calories Restaurant Sandwiches Fat (grams) The scatter plot at the left shows the amounts of fat (in grams) and the numbers of calories in 2 restaurant sandwiches. a. How man calories are in the sandwich that contains 7 grams of fat? Restaurant Sandwiches Draw a horizontal line from the point that has 8 an -value of 7. It 7 crosses the -ais at 4. So, the sandwich has 4 calories. b. How man grams of fat are in the sandwich that contains 6 calories? Draw a vertical line from the point that has a -value of 6. It crosses the -ais at 3. Calories Fat (grams) So, the sandwich has 3 grams of fat. c. What tends to happen to the number of calories as the number of grams of fat increases? Looking at the graph, the plotted points go up from left to right. So, as the number of grams of fat increases, the number of calories increases. Eercises 8 and 9. WHAT IF? A sandwich has 6 calories. Based on the scatter plot in Eample, how man grams of fat would ou epect the sandwich to have? Eplain our reasoning. 374 Chapter 9 Data Analsis and Displas

4 A scatter plot can show that a relationship eists between two data sets. Positive Linear Negative Linear Nonlinear Relationship Relationship Relationship No Relationship O O O O The points lie close to a line. As increases, increases. The points lie close to a line. As increases, decreases. The points lie in the shape of a curve. The points show no pattern. EXAMPLE 2 Identifing Relationships Describe the relationship between the data. Identif an outliers, gaps, or clusters. a. television size and price b. age and number of pets owned Television Size and Price Age and Pets Owned Price (dollars) Number of pets owned Television size (inches) Person s age (ears) The points appear to lie close to a line. As increases, increases. So, the scatter plot shows a positive linear relationship. There is an outlier at (7, 22), a cluster of data under $, and a gap in the data from $ to $. The points show no pattern. So, the scatter plot shows no relationship. There are no obvious outliers, gaps, or clusters in the data. Eercises 2 2. Make a scatter plot of the data and describe the relationship between the data. Identif an outliers, gaps, or clusters. Stud Time (min), Test Score, Section 9. Scatter Plots 37

5 9. Eercises Help with Homework. VOCABULARY What tpe of data do ou need to make a scatter plot? Eplain. 2. REASONING How can ou identif an outlier in a scatter plot? LOGIC Describe the relationship ou would epect between the data. Eplain. 3. shoe size of a student and the student s IQ 4. time since a train s departure and the distance to its destination. height of a bouncing ball and the time since it was dropped 6. number of toppings on a pizza and the price of the pizza 9+(-6)=3 3+(-3)= 4+(-9)= 9+(-)= 7. JEANS The table shows the average price (in dollars) of jeans sold at different stores and the number of pairs of jeans sold at each store in one month. Average Price Number Sold a. Write the ordered pairs from the table and plot them in a coordinate plane. b. Describe the relationship between the two data sets. 8. SUVS The scatter plot shows the numbers of sport utilit vehicles sold in a cit from 29 to 24. a. In what ear were SUVs sold? b. About how man SUVs were sold in 23? c. Describe the relationship shown b the data. Number sold SUV Sales Year Earnings of a Food Server Earnings (dollars) Hours worked 9. EARNINGS The scatter plot shows the total earnings (wages and tips) of a food server during one da. a. About how man hours must the server work to earn $7? b. About how much did the server earn for hours of work? c. Describe the relationship shown b the data. 376 Chapter 9 Data Analsis and Displas

6 2 Describe the relationship between the data. Identif an outliers, gaps, or clusters HONEY The table shows the average price per pound for hone in the United States from 29 to 22. What tpe of relationship do the data show? Year, Average Price per Pound, $4.6 $4.8 $. $.3 4. TEST SCORES The scatter plot shows the numbers of minutes spent studing and the test scores for a science class. (a) What tpe of relationship do the data show? (b) Interpret the relationship.. OPEN-ENDED Describe a set of real-life data that has a negative linear relationship. Stud Time and Test Scores Test scores Stud time (minutes) 6. PROBLEM SOLVING The table shows the memor capacities (in gigabtes) and prices (in dollars) of 7-inch tablet computers at a store. (a) Make a scatter plot of the data. Then describe the relationship between the data. (b) Identif an outliers, gaps, or clusters. Eplain wh ou think the eist. Memor (GB), Price (dollars), Sales of sunglasses and beach towels at a store show a positive linear relationship in the summer. Does this mean that the sales of one item cause the sales of the other item to increase? Eplain. Use a graph to solve the equation. Check our solution. (Section.4) 8. = = = MULTIPLE CHOICE When graphing a proportional relationship represented b = m, which point is not on the graph? (Section 4.3) A (, ) B (, m) C (, m) D (2, 2m) Section 9. Scatter Plots 377

Essential Question How can you use a scatter plot and a line of fit to make conclusions about data?

Essential Question How can you use a scatter plot and a line of fit to make conclusions about data? . Scatter Plots and Lines of Fit Essential Question How can ou use a scatter plot and a line of fit to make conclusions about data? A scatter plot is a graph that shows the relationship between two data

More information

ACTIVITY: Using a Table to Plot Points

ACTIVITY: Using a Table to Plot Points .5 Graphing Linear Equations in Standard Form equation a + b = c? How can ou describe the graph of the ACTIVITY: Using a Table to Plot Points Work with a partner. You sold a total of $6 worth of tickets

More information

Comparing Linear and Nonlinear Functions 5.5. ACTIVITY: Finding Patterns for Similar Figures. How can you recognize when a pattern

Comparing Linear and Nonlinear Functions 5.5. ACTIVITY: Finding Patterns for Similar Figures. How can you recognize when a pattern 5.5 Comparing Linear and Nonlinear Functions in real life is linear or nonlinear? How can ou recognize when a pattern ACTIVITY: Finding Patterns for Similar Figures Work with a partner. Cop and complete

More information

How can you write an equation of a line when you are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines

How can you write an equation of a line when you are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines .7 Writing Equations in Point-Slope Form How can ou write an equation of a line when ou are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines Work with a partner. Sketch the

More information

Systems of Linear Inequalities

Systems of Linear Inequalities . Sstems of Linear Inequalities sstem of linear inequalities? How can ou sketch the graph of a ACTIVITY: Graphing Linear Inequalities Work with a partner. Match the linear inequalit with its graph. + Inequalit

More information

Name Date. and y = 5.

Name Date. and y = 5. Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five

More information

Chapter 9. Chapter 9 Opener. Section 9.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 371) m = = = = 9.1 Activity (pp.

Chapter 9. Chapter 9 Opener. Section 9.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 371) m = = = = 9.1 Activity (pp. Chapter 9 Opener Tr It Yourself (p. 7).. To plot (, ), start at the origin and move unit right and units up. The point is in Quadrant I.. To plot (, ), start at the origin and move units left and units

More information

4.4 Scatter Plots and Lines of Fit 4.5 Analyzing Lines of Fit 4.6 Arithmetic Sequences 4.7 Piecewise Functions

4.4 Scatter Plots and Lines of Fit 4.5 Analyzing Lines of Fit 4.6 Arithmetic Sequences 4.7 Piecewise Functions Writing Linear Functions. Writing Equations in Slope-Intercept Form. Writing Equations in Point-Slope Form.3 Writing Equations of Parallel and Perpendicular Lines. Scatter Plots and Lines of Fit.5 Analzing

More information

ACTIVITY: Comparing Types of Decay

ACTIVITY: Comparing Types of Decay 6.6 Eponential Deca eponential deca? What are the characteristics of 1 ACTIVITY: Comparing Tpes of Deca Work with a partner. Describe the pattern of deca for each sequence and graph. Which of the patterns

More information

3.2 Understanding Relations and Functions-NOTES

3.2 Understanding Relations and Functions-NOTES Name Class Date. Understanding Relations and Functions-NOTES Essential Question: How do ou represent relations and functions? Eplore A1.1.A decide whether relations represented verball, tabularl, graphicall,

More information

Using Intercept Form

Using Intercept Form 8.5 Using Intercept Form Essential Question What are some of the characteristics of the graph of f () = a( p)( q)? Using Zeros to Write Functions Work with a partner. Each graph represents a function of

More information

Fair Game Review. Chapter 5. Input, x Output, y. 1. Input, x Output, y. Describe the pattern of inputs x and outputs y.

Fair Game Review. Chapter 5. Input, x Output, y. 1. Input, x Output, y. Describe the pattern of inputs x and outputs y. Name Date Chapter Fair Game Review Describe the pattern of inputs and outputs.. Input, utput,. 8 Input, utput,. Input, 9. utput, 8 Input, utput, 9. The table shows the number of customers in hours. Describe

More information

Characteristics of Quadratic Functions

Characteristics of Quadratic Functions . Characteristics of Quadratic Functions Essential Question What tpe of smmetr does the graph of f() = a( h) + k have and how can ou describe this smmetr? Parabolas and Smmetr Work with a partner. a. Complete

More information

Discrete and Continuous Domains

Discrete and Continuous Domains . Discrete and Continuous Domains How can ou decide whether the domain of a function is discrete or continuous? EXAMPLE: Discrete and Continuous Domains In Activities and in Section., ou studied two real-life

More information

Solving Systems of Linear Equations by Graphing

Solving Systems of Linear Equations by Graphing . Solving Sstems of Linear Equations b Graphing How can ou solve a sstem of linear equations? ACTIVITY: Writing a Sstem of Linear Equations Work with a partner. Your famil starts a bed-and-breakfast. The

More information

Comparing Linear, Exponential, and Quadratic Functions

Comparing Linear, Exponential, and Quadratic Functions . Comparing Linear, Eponential, and Quadratic Functions How can ou compare the growth rates of linear, eponential, and quadratic functions? ACTIVITY: Comparing Speeds Work with a partner. Three cars start

More information

Graphing and Writing Linear Equations

Graphing and Writing Linear Equations Graphing and Writing Linear Equations. Graphing Linear Equations. Slope of a Line. Graphing Linear Equations in Slope-Intercept Form. Graphing Linear Equations in Standard Form. Writing Equations in Slope-Intercept

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name Date Chapter 3 Maintaining Mathematical Proficienc Plot the point in a coordinate plane. Describe the location of the point. 1. A( 3, 1). B (, ) 3. C ( 1, 0). D ( 5, ) 5. Plot the point that is on

More information

Solving Quadratic Equations by Graphing 9.1. ACTIVITY: Solving a Quadratic Equation by Graphing. How can you use a graph to solve a quadratic

Solving Quadratic Equations by Graphing 9.1. ACTIVITY: Solving a Quadratic Equation by Graphing. How can you use a graph to solve a quadratic 9. Solving Quadratic Equations b Graphing equation in one variable? How can ou use a graph to solve a quadratic Earlier in the book, ou learned that the -intercept of the graph of = a + b variables is

More information

Name: Class: Date: Mini-Unit. Data & Statistics. Investigation 1: Variability & Associations in Numerical Data. Practice Problems

Name: Class: Date: Mini-Unit. Data & Statistics. Investigation 1: Variability & Associations in Numerical Data. Practice Problems Mini-Unit Data & Statistics Investigation 1: Variability & Associations in Numerical Data Practice Problems Directions: Please complete the necessary problems to earn a maximum of 5 points according to

More information

Essential Question How can you solve a system of linear equations? $15 per night. Cost, C (in dollars) $75 per Number of. Revenue, R (in dollars)

Essential Question How can you solve a system of linear equations? $15 per night. Cost, C (in dollars) $75 per Number of. Revenue, R (in dollars) 5.1 Solving Sstems of Linear Equations b Graphing Essential Question How can ou solve a sstem of linear equations? Writing a Sstem of Linear Equations Work with a partner. Your famil opens a bed-and-breakfast.

More information

Graph Quadratic Functions in Standard Form

Graph Quadratic Functions in Standard Form TEKS 4. 2A.4.A, 2A.4.B, 2A.6.B, 2A.8.A Graph Quadratic Functions in Standard Form Before You graphed linear functions. Now You will graph quadratic functions. Wh? So ou can model sports revenue, as in

More information

Functions. Essential Question What is a function? Work with a partner. Functions can be described in many ways.

Functions. Essential Question What is a function? Work with a partner. Functions can be described in many ways. . Functions Essential Question What is a function? A relation pairs inputs with outputs. When a relation is given as ordered pairs, the -coordinates are inputs and the -coordinates are outputs. A relation

More information

Lesson 1 Homework Practice

Lesson 1 Homework Practice Lesson 1 Homework Practice Scatter Plots Interpret each scatter plot. 1. Games Won 1 8 6 4 2 1 2 3 4 5 Average Game Attendance 2. Car Value (% cost new) 1 9 8 7 6 5 4 3 2 1 2 4 6 8 1 Car Age (r) 3. Pumpkin

More information

1Write and graph. 2Solve problems. Now. Then. Why? New Vocabulary

1Write and graph. 2Solve problems. Now. Then. Why? New Vocabulary Direct Variation Then You found rates of change of linear functions. (Lesson -) Now Write and graph direct variation equations. Solve problems involving direct variation. Wh? Bianca is saving her mone

More information

Solving Polynomial Equations Exponential Growth in Factored Form

Solving Polynomial Equations Exponential Growth in Factored Form 7.5 Solving Polnomial Equations Eponential Growth in Factored Form is written in factored form? How can ou solve a polnomial equation that Two polnomial equations are equivalent when the have the same

More information

1.7 Inverse Functions

1.7 Inverse Functions 71_0107.qd 1/7/0 10: AM Page 17 Section 1.7 Inverse Functions 17 1.7 Inverse Functions Inverse Functions Recall from Section 1. that a function can be represented b a set of ordered pairs. For instance,

More information

Chapter 9 BUILD YOUR VOCABULARY

Chapter 9 BUILD YOUR VOCABULARY C H A P T E R 9 BUILD YUR VCABULARY Chapter 9 This is an alphabetical list of new vocabular terms ou will learn in Chapter 9. As ou complete the stud notes for the chapter, ou will see Build Your Vocabular

More information

Learning Objective: We will construct and interpret scatterplots (G8M6L4)

Learning Objective: We will construct and interpret scatterplots (G8M6L4) Learning Objective: We will construct and interpret scatterplots (G8ML) Concept Development: A Scatter Plot is a graph of numerical data on two variables. Eamples: -- The number of hours ou stud for a

More information

Functions. Essential Question What is a function?

Functions. Essential Question What is a function? 3. Functions COMMON CORE Learning Standard HSF-IF.A. Essential Question What is a function? A relation pairs inputs with outputs. When a relation is given as ordered pairs, the -coordinates are inputs

More information

Fair Game Review. Chapter 2. and y = 5. Evaluate the expression when x = xy 2. 4x. Evaluate the expression when a = 9 and b = 4.

Fair Game Review. Chapter 2. and y = 5. Evaluate the expression when x = xy 2. 4x. Evaluate the expression when a = 9 and b = 4. Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five

More information

Essential Question How can you use a quadratic function to model a real-life situation?

Essential Question How can you use a quadratic function to model a real-life situation? 3. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A..A A..E A..A A..B A..C Modeling with Quadratic Functions Essential Question How can ou use a quadratic function to model a real-life situation? Work with a partner.

More information

Algebra 1 Practice Test Modeling with Linear Functions Unit 6. Name Period Date

Algebra 1 Practice Test Modeling with Linear Functions Unit 6. Name Period Date Name Period Date Vocabular: Define each word and give an example.. Correlation 2. Residual plot. Translation Short Answer: 4. Statement: If a strong correlation is present between two variables, causation

More information

6.2b Homework: Fit a Linear Model to Bivariate Data

6.2b Homework: Fit a Linear Model to Bivariate Data 6.2b Homework: Fit a Linear Model to Bivariate Data Directions: For the following problems, draw a line of best fit, write a prediction function, and use your function to make predictions. Prior to drawing

More information

Use Properties of Exponents

Use Properties of Exponents 4. Georgia Performance Standard(s) MMAa Your Notes Use Properties of Eponents Goal p Simplif epressions involving powers. VOCABULARY Scientific notation PROPERTIES OF EXPONENTS Let a and b be real numbers

More information

Lesson Remember. Finding Domain and Range from a Graph EXAMPLE. Key Vocabulary

Lesson Remember. Finding Domain and Range from a Graph EXAMPLE. Key Vocabulary 0. Lesson Ke Vocabular function domain range function form Functions A function is a relationship that pairs each input with eactl one output. The domain is the set of all possible input values. The range

More information

Linear Functions. Essential Question How can you determine whether a function is linear or nonlinear?

Linear Functions. Essential Question How can you determine whether a function is linear or nonlinear? . Linear Functions Essential Question How can ou determine whether a function is linear or nonlinear? Finding Patterns for Similar Figures Work with a partner. Cop and complete each table for the sequence

More information

Chapter 11. Correlation and Regression

Chapter 11. Correlation and Regression Chapter 11 Correlation and Regression Correlation A relationship between two variables. The data can be represented b ordered pairs (, ) is the independent (or eplanator) variable is the dependent (or

More information

Chapter 4. Chapter 4 Opener. Section 4.1. Big Ideas Math Blue Worked-Out Solutions. x 2. Try It Yourself (p. 147) x 0 1. y ( ) x 2

Chapter 4. Chapter 4 Opener. Section 4.1. Big Ideas Math Blue Worked-Out Solutions. x 2. Try It Yourself (p. 147) x 0 1. y ( ) x 2 Chapter Chapter Opener Tr It Yourself (p. 7). As the input decreases b, the output increases b.. Input As the input increases b, the output increases b.. As the input decreases b, the output decreases

More information

Analytic Geometry 300 UNIT 9 ANALYTIC GEOMETRY. An air traffi c controller uses algebra and geometry to help airplanes get from one point to another.

Analytic Geometry 300 UNIT 9 ANALYTIC GEOMETRY. An air traffi c controller uses algebra and geometry to help airplanes get from one point to another. UNIT 9 Analtic Geometr An air traffi c controller uses algebra and geometr to help airplanes get from one point to another. 00 UNIT 9 ANALYTIC GEOMETRY Copright 00, K Inc. All rights reserved. This material

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Chapter Maintaining Mathematical Proficienc Find the -intercept of the graph of the linear equation. 1. = + 3. = 3 + 5 3. = 10 75. = ( 9) 5. 7( 10) = +. 5 + 15 = 0 Find the distance between the two points.

More information

Chapter Fair Game Review Find the missing value in the table. Big Ideas Math Blue 119

Chapter Fair Game Review Find the missing value in the table. Big Ideas Math Blue 119 Name Date Chapter 6 Fair Game Review Find the missing value in the table... 5 7 5 9 7 6 8.. 6 9 6 8 8 9 8 8 5. 6..5 9.5 5.5 6 5.8 5.8.8.6. Copright Big Ideas Learning, LLC Big Ideas Math Blue 9 Name Date

More information

Which of the following is an irrational number? a) 2.8 b) 19

Which of the following is an irrational number? a) 2.8 b) 19 Which of the following is an irrational number? a) 2.8 b) 19 c)!! d) 81 A discounted ticket for a football game costs $12.50 less than the original price p. You pay $63 for a discounted ticket. Write and

More information

Fair Game Review. Chapter = How many calculators are sold when the profit is $425? Solve the equation. Check your solution.

Fair Game Review. Chapter = How many calculators are sold when the profit is $425? Solve the equation. Check your solution. Name Date Chapter 4 Fair Game Review Solve the equation. Check our solution.. 8 3 = 3 2. 4a + a = 2 3. 9 = 4( 3k 4) 7k 4. ( m) 2 5 6 2 = 8 5. 5 t + 8t = 3 6. 3 5h 2 h + 4 = 0 2 7. The profit P (in dollars)

More information

Introduction Direct Variation Rates of Change Scatter Plots. Introduction. EXAMPLE 1 A Mathematical Model

Introduction Direct Variation Rates of Change Scatter Plots. Introduction. EXAMPLE 1 A Mathematical Model APPENDIX B Mathematical Modeling B1 Appendi B Mathematical Modeling B.1 Modeling Data with Linear Functions Introduction Direct Variation Rates of Change Scatter Plots Introduction The primar objective

More information

Chapter 4 ( 2, 2 ). Chapter 4 Opener. Section 4.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 141) = = = = 15. The solution checks.

Chapter 4 ( 2, 2 ). Chapter 4 Opener. Section 4.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 141) = = = = 15. The solution checks. Chapter Chapter Opener Tr It Yourself (p. ). ab = ( ) = ( ) = = = =. a b = ( ). a b = = = = + = + = + 9 =, or. a ( b a ). Point Q is on the -ais, units up from the origin. So, the -coordinate is, and the

More information

Nonproportional. Real-World Video

Nonproportional. Real-World Video Nonproportional Relationships MODULE 17? ESSENTIAL QUESTION How can ou use nonproportional relationships to solve real-world problems? LESSON 17.1 Representing Linear Nonproportional Relationships 8.F.3

More information

Represent Relations and Functions

Represent Relations and Functions TEKS. a., a., a.5, A..A Represent Relations and Functions Before You solved linear equations. Now You will represent relations and graph linear functions. Wh? So ou can model changes in elevation, as in

More information

Nonproportional Relationships. Real-World Video

Nonproportional Relationships. Real-World Video Nonproportional Relationships? MODULE LESSON.1 ESSENTIAL QUESTION Representing Linear Nonproportional Relationships How can ou use nonproportional relationships to solve real-world problems? 8.F.1.3 LESSON.

More information

Can a system of linear equations have no solution? Can a system of linear equations have many solutions?

Can a system of linear equations have no solution? Can a system of linear equations have many solutions? 5. Solving Special Sstems of Linear Equations Can a sstem of linear equations have no solution? Can a sstem of linear equations have man solutions? ACTIVITY: Writing a Sstem of Linear Equations Work with

More information

4 B. 4 D. 4 F. 3. How can you use the graph of a quadratic equation to determine the number of real solutions of the equation?

4 B. 4 D. 4 F. 3. How can you use the graph of a quadratic equation to determine the number of real solutions of the equation? 3.1 Solving Quadratic Equations COMMON CORE Learning Standards HSA-SSE.A. HSA-REI.B.b HSF-IF.C.8a Essential Question Essential Question How can ou use the graph of a quadratic equation to determine the

More information

11.1 Inverses of Simple Quadratic and Cubic Functions

11.1 Inverses of Simple Quadratic and Cubic Functions Locker LESSON 11.1 Inverses of Simple Quadratic and Cubic Functions Teas Math Standards The student is epected to: A..B Graph and write the inverse of a function using notation such as f (). Also A..A,

More information

4.2 Parabolas. Explore Deriving the Standard-Form Equation. Houghton Mifflin Harcourt Publishing Company. (x - p) 2 + y 2 = (x + p) 2

4.2 Parabolas. Explore Deriving the Standard-Form Equation. Houghton Mifflin Harcourt Publishing Company. (x - p) 2 + y 2 = (x + p) 2 COMMON CORE. d Locker d LESSON Parabolas Common Core Math Standards The student is epected to: COMMON CORE A-CED.A. Create equations in two or more variables to represent relationships between quantities;

More information

How can you use multiplication or division to solve an equation? ACTIVITY: Finding Missing Dimensions

How can you use multiplication or division to solve an equation? ACTIVITY: Finding Missing Dimensions 7.3 Solving Equations Using Multiplication or Division How can you use multiplication or division to solve an equation? 1 ACTIVITY: Finding Missing Dimensions Work with a partner. Describe how you would

More information

How can you use multiplication or division to solve an inequality? ACTIVITY: Using a Table to Solve an Inequality

How can you use multiplication or division to solve an inequality? ACTIVITY: Using a Table to Solve an Inequality . Solving Inequalities Using Multiplication or Division How can you use multiplication or division to solve an inequality? 1 ACTIVITY: Using a Table to Solve an Inequality Work with a partner. Copy and

More information

ACCELERATED MATHEMATICS CHAPTER 7 NON-PROPORTIONAL LINEAR RELATIONSHIPS TOPICS COVERED:

ACCELERATED MATHEMATICS CHAPTER 7 NON-PROPORTIONAL LINEAR RELATIONSHIPS TOPICS COVERED: ACCELERATED MATHEMATICS CHAPTER 7 NON-PROPORTIONAL LINEAR RELATIONSHIPS TOPICS COVERED: Representing Linear Non-Proportional Equations Slope & -Intercept Graphing Using Slope & -Intercept Proportional

More information

Writing Equations in One Variable

Writing Equations in One Variable 7.1 Writing Equations in One Variable solve the word problem? How does rewriting a word problem help you 1 ACTIVITY: Rewriting a Word Problem Work with a partner. Read the problem several times. Think

More information

Modeling with Exponential and Logarithmic Functions 6.7. Essential Question How can you recognize polynomial, exponential, and logarithmic models?

Modeling with Exponential and Logarithmic Functions 6.7. Essential Question How can you recognize polynomial, exponential, and logarithmic models? .7 Modeling with Eponential and Logarithmic Functions Essential Question How can ou recognize polnomial, eponential, and logarithmic models? Recognizing Different Tpes of Models Work with a partner. Match

More information

Graph Linear Inequalities in Two Variables. You solved linear inequalities in one variable. You will graph linear inequalities in two variables.

Graph Linear Inequalities in Two Variables. You solved linear inequalities in one variable. You will graph linear inequalities in two variables. TEKS.8 a.5 Before Now Graph Linear Inequalities in Two Variables You solved linear inequalities in one variable. You will graph linear inequalities in two variables. Wh? So ou can model data encoding,

More information

How can you determine the number of solutions of a quadratic equation of the form ax 2 + c = 0? ACTIVITY: The Number of Solutions of ax 2 + c = 0

How can you determine the number of solutions of a quadratic equation of the form ax 2 + c = 0? ACTIVITY: The Number of Solutions of ax 2 + c = 0 9. Solving Quadratic Equations Using Square Roots How can ou determine the number of solutions of a quadratic equation of the form a + c = 0? ACTIVITY: The Number of Solutions of a + c = 0 Work with a

More information

You studied exponential growth and decay functions.

You studied exponential growth and decay functions. TEKS 7. 2A.4.B, 2A..B, 2A..C, 2A..F Before Use Functions Involving e You studied eponential growth and deca functions. Now You will stud functions involving the natural base e. Wh? So ou can model visibilit

More information

SWBAT recognize and represent proportional relationship between quantities (7.RP.2). reason abstractly and quantitatively (MP #2).

SWBAT recognize and represent proportional relationship between quantities (7.RP.2). reason abstractly and quantitatively (MP #2). Name Period Date th Grade Mathematics Ms. Ullian, Ms. Ferraro, Mr. Guzzio - SWBAT recognize and represent proportional relationship between quantities (.RP.). reason abstractl and quantitativel (MP #).

More information

3-1. Solving Systems Using Tables and Graphs. Concept Summary. Graphical Solutions of Linear Systems VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING

3-1. Solving Systems Using Tables and Graphs. Concept Summary. Graphical Solutions of Linear Systems VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING 3- Solving Sstems Using Tables and Graphs TEKS FOCUS VOCABULARY Foundational to TEKS (3)(A) Formulate sstems of equations, including sstems consisting of three linear equations in three variables and sstems

More information

) approaches e

) approaches e COMMON CORE Learning Standards HSF-IF.C.7e HSF-LE.B.5. USING TOOLS STRATEGICALLY To be proficient in math, ou need to use technological tools to eplore and deepen our understanding of concepts. The Natural

More information

Algebra 1. Standard Create and Analyze Tables and Graphs. Categories Tables Graphs Context Problems Making Predictions

Algebra 1. Standard Create and Analyze Tables and Graphs. Categories Tables Graphs Context Problems Making Predictions Algebra Standard Create and Analze Tables and Graphs Categories Tables Graphs Contet Problems Making Predictions Summative Assessment Date: Wednesda, August 9 th Page Create and Analze Tables and Graphs

More information

Solving Special Systems of Linear Equations

Solving Special Systems of Linear Equations .....5 Solving Sstems of Linear Equations Solving Sstems of Linear Equations b Graphing Solving Sstems of Linear Equations b Substitution Solving Sstems of Linear Equations b Elimination Solving Special

More information

LESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II

LESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS

More information

Linear Relations and Functions

Linear Relations and Functions Linear Relations and Functions Why? You analyzed relations and functions. (Lesson 2-1) Now Identify linear relations and functions. Write linear equations in standard form. New Vocabulary linear relations

More information

Mini-Lecture 8.1 Solving Quadratic Equations by Completing the Square

Mini-Lecture 8.1 Solving Quadratic Equations by Completing the Square Mini-Lecture 8.1 Solving Quadratic Equations b Completing the Square Learning Objectives: 1. Use the square root propert to solve quadratic equations.. Solve quadratic equations b completing the square.

More information

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Read To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Find these vocabular words in Lesson 5-1 and the Multilingual Glossar. Vocabular quadratic function parabola verte

More information

15.2 Graphing Logarithmic

15.2 Graphing Logarithmic _ - - - - - - Locker LESSON 5. Graphing Logarithmic Functions Teas Math Standards The student is epected to: A.5.A Determine the effects on the ke attributes on the graphs of f () = b and f () = log b

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name Date Chapter 5 Maintaining Mathematical Proficienc Graph the equation. 1. + =. = 3 3. 5 + = 10. 3 = 5. 3 = 6. 3 + = 1 Solve the inequalit. Graph the solution. 7. a 3 > 8. c 9. d 5 < 3 10. 8 3r 5 r

More information

LESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II

LESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS

More information

Systems of Linear and Quadratic Equations. Check Skills You ll Need. y x. Solve by Graphing. Solve the following system by graphing.

Systems of Linear and Quadratic Equations. Check Skills You ll Need. y x. Solve by Graphing. Solve the following system by graphing. NY- Learning Standards for Mathematics A.A. Solve a sstem of one linear and one quadratic equation in two variables, where onl factoring is required. A.G.9 Solve sstems of linear and quadratic equations

More information

10.7. Interpret the Discriminant. For Your Notebook. x5 2b 6 Ï} b 2 2 4ac E XAMPLE 1. Use the discriminant KEY CONCEPT

10.7. Interpret the Discriminant. For Your Notebook. x5 2b 6 Ï} b 2 2 4ac E XAMPLE 1. Use the discriminant KEY CONCEPT 10.7 Interpret the Discriminant Before You used the quadratic formula. Now You will use the value of the discriminant. Wh? So ou can solve a problem about gmnastics, as in E. 49. Ke Vocabular discriminant

More information

1.) The number of points a basketball player scored each game for one week is recorded. Which is a not a statistical question for the situation?

1.) The number of points a basketball player scored each game for one week is recorded. Which is a not a statistical question for the situation? 6 th Grade Math Common Assessment: Chapter 6 Name: Date 6.SP.1 1.) The number of points a basketball player scored each game for one week is recorded. Which is a not a statistical question for the situation?

More information

Name PD. Linear Functions

Name PD. Linear Functions Name PD Linear Functions Finding the Slope of a Line The steepness of the line is the ratio of rise to run, or vertical change to horizontal change, for this step. We call this ratio the slope of the line.

More information

Focusing on Linear Functions and Linear Equations

Focusing on Linear Functions and Linear Equations Focusing on Linear Functions and Linear Equations In grade, students learn how to analyze and represent linear functions and solve linear equations and systems of linear equations. They learn how to represent

More information

Write in simplest form. New Vocabulary rate of change

Write in simplest form. New Vocabulary rate of change -. Plan bjectives To find rates of change from tables and graphs To find slope Eamples Finding Rate of Change Using a Table Finding Rate of Change Using a Graph Finding Slope Using a Graph Finding Slope

More information

Inverse of a Function

Inverse of a Function . Inverse o a Function Essential Question How can ou sketch the graph o the inverse o a unction? Graphing Functions and Their Inverses CONSTRUCTING VIABLE ARGUMENTS To be proicient in math, ou need to

More information

3.2 Introduction to Functions

3.2 Introduction to Functions 8 CHAPTER Graphs and Functions Write each statement as an equation in two variables. Then graph each equation. 97. The -value is more than three times the -value. 98. The -value is - decreased b twice

More information

3.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS

3.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS Section. Logarithmic Functions and Their Graphs 7. LOGARITHMIC FUNCTIONS AND THEIR GRAPHS Ariel Skelle/Corbis What ou should learn Recognize and evaluate logarithmic functions with base a. Graph logarithmic

More information

1.5. Analyzing Graphs of Functions. The Graph of a Function. What you should learn. Why you should learn it. 54 Chapter 1 Functions and Their Graphs

1.5. Analyzing Graphs of Functions. The Graph of a Function. What you should learn. Why you should learn it. 54 Chapter 1 Functions and Their Graphs 0_005.qd /7/05 8: AM Page 5 5 Chapter Functions and Their Graphs.5 Analzing Graphs of Functions What ou should learn Use the Vertical Line Test for functions. Find the zeros of functions. Determine intervals

More information

Fair Game Review. Chapter 8. Graph the linear equation. Big Ideas Math Algebra Record and Practice Journal

Fair Game Review. Chapter 8. Graph the linear equation. Big Ideas Math Algebra Record and Practice Journal Name Date Chapter Graph the linear equation. Fair Game Review. =. = +. =. =. = +. = + Copright Big Ideas Learning, LLC Big Ideas Math Algebra Name Date Chapter Fair Game Review (continued) Evaluate the

More information

Vocabulary. Fitting a Line to Data. Lesson 2-2 Linear Models

Vocabulary. Fitting a Line to Data. Lesson 2-2 Linear Models Lesson 2-2 Linear Models BIG IDEA The sum of squared deviations is a statistic for determining which of two lines fi ts the data better. A linear function is a set of ordered pairs (, ) satisfing an equation

More information

Properties of the Graph of a Quadratic Function. has a vertex with an x-coordinate of 2 b } 2a

Properties of the Graph of a Quadratic Function. has a vertex with an x-coordinate of 2 b } 2a 0.2 Graph 5 a 2 b c Before You graphed simple quadratic functions. Now You will graph general quadratic functions. Wh? So ou can investigate a cable s height, as in Eample 4. Ke Vocabular minimum value

More information

EVALUATING POLYNOMIAL FUNCTIONS

EVALUATING POLYNOMIAL FUNCTIONS Page 1 of 8 6.2 Evaluating and Graphing Polnomial Functions What ou should learn GOAL 1 Evaluate a polnomial function. GOAL 2 Graph a polnomial function, as applied in Eample 5. Wh ou should learn it To

More information

6. 4 : 5 is in simplest form because 4 and 5 have no. common factors. 4 : : 5 3. and 7 : : 14 2

6. 4 : 5 is in simplest form because 4 and 5 have no. common factors. 4 : : 5 3. and 7 : : 14 2 9. Let the number of balloons be. Total cost of balloons: $(.0) Cost of banner: $ Total ependiture of committee: $(.0 ) The most the committee can spend is $:.0.0.0 90.0.0 90.0.7 The can bu at most balloons.

More information

Linear and Nonlinear Systems of Equations. The Method of Substitution. Equation 1 Equation 2. Check (2, 1) in Equation 1 and Equation 2: 2x y 5?

Linear and Nonlinear Systems of Equations. The Method of Substitution. Equation 1 Equation 2. Check (2, 1) in Equation 1 and Equation 2: 2x y 5? 3330_070.qd 96 /5/05 Chapter 7 7. 9:39 AM Page 96 Sstems of Equations and Inequalities Linear and Nonlinear Sstems of Equations What ou should learn Use the method of substitution to solve sstems of linear

More information

Summary and Vocabulary

Summary and Vocabulary Chapter 2 Chapter 2 Summar and Vocabular The functions studied in this chapter are all based on direct and inverse variation. When k and n >, formulas of the form = k n define direct-variation functions,

More information

Graphing Linear Equations

Graphing Linear Equations 1-3 BJECTIVES Graph linear equations. Find the - and -intercepts of a line. Find the slope of a line through two points. Find zeros of linear functions. Graphing Linear Equations AGRICULTURE American farmers

More information

c. Find the slope and y-intercept of the graph of the linear equation. Then sketch its graph.

c. Find the slope and y-intercept of the graph of the linear equation. Then sketch its graph. Name Solve. End-of-Course. 7 =. 5 c =. One cell phone plan charges $0 per month plus $0.5 per minute used. A second cell phone plan charges $5 per month plus $0.0 per minute used. Write and solve an equation

More information

3.1 Graph Quadratic Functions

3.1 Graph Quadratic Functions 3. Graph Quadratic Functions in Standard Form Georgia Performance Standard(s) MMA3b, MMA3c Goal p Use intervals of increase and decrease to understand average rates of change of quadratic functions. Your

More information

ONLINE PAGE PROOFS. Relationships between two numerical variables

ONLINE PAGE PROOFS. Relationships between two numerical variables 14 Relationships between two numerical variables 14.1 Kick off with CAS 14.2 Scatterplots and basic correlation 14.3 Further correlation coefficients 14.4 Making predictions 14.5 Review 14.1 Kick off with

More information

National 5 Portfolio Applications Standard Deviation and Scattergraphs

National 5 Portfolio Applications Standard Deviation and Scattergraphs National 5 Portfolio Applications 1.4 - Standard Deviation and Scattergraphs N5 Section A - Revision This section will help you revise previous learning which is required in this topic. R1 I can calculate

More information

Simplifying Rational Expressions

Simplifying Rational Expressions .3 Simplifying Rational Epressions What are the ecluded values of a rational epression? How can you simplify a rational epression? ACTIVITY: Simplifying a Rational Epression Work with a partner. Sample:

More information

R = { } Fill-in-the-Table with the missing vocabulary terms: 1) 2) Fill-in-the-blanks: Function

R = { } Fill-in-the-Table with the missing vocabulary terms: 1) 2) Fill-in-the-blanks: Function Name: Date: / / QUIZ DAY! Fill-in-the-Table with the missing vocabular terms: ) ) Input Fill-in-the-blanks: 3) Output Function A special tpe of where there is one and onl one range () value for ever domain

More information

Writing Equations in Point-Slope Form

Writing Equations in Point-Slope Form . Writing Equations in Point-Slope Form Essential Question How can ou write an equation of a line when ou are given the slope and a point on the line? Writing Equations of Lines Work with a partner. Sketch

More information

Name Date. Work with a partner. Each graph shown is a transformation of the parent function

Name Date. Work with a partner. Each graph shown is a transformation of the parent function 3. Transformations of Eponential and Logarithmic Functions For use with Eploration 3. Essential Question How can ou transform the graphs of eponential and logarithmic functions? 1 EXPLORATION: Identifing

More information

Solving Multi-Step Inequalities

Solving Multi-Step Inequalities . Solving Multi-Step Inequalities How can ou use an inequalit to describe the area and perimeter of a composite figure? ACTIVITY: Areas and Perimeters of Composite Figures Wor with a partner. a. For what

More information