2.2 Contextualizing Linear Functions
|
|
- Maurice Oliver
- 6 years ago
- Views:
Transcription
1 2.2 izing Linear Functions Last unit we defined a linear function in several different ways: A function whose graph is a straight line, A function whose rate of change is constant, or A function whose equation is of the form where represents the slope and represents the y intercept. We ll now begin exploring the difference aspects of a linear function and how each piece affects the function as a whole. Input (Independent Variable) and Output (Dependent Variable) Since a function is a rule that assigns to each input exactly one output, it is crucial to identify and understand what the input and output are in the multiple forms of a function. Let s look at the following linear functions written in different forms. Example 1 The number of grapes depends on the number of branches off the main vine and is represented by this equation: Example 2 A dairy farmer can produce 25 gallons of milk from 3 cows Example 3 The cost for joining a gym includes a start up fee plus dues every month In example 1, what is the input? What do we start with? What comes first? The branches of the vine. Once we have branches, those branches then produce grapes. So the input, the thing we start with, is the independent variable. Cost in $ Months The independent variable is the variable that could be anything (at least anything within the domain). We could have any number of branches we want and the branches produce, or output, the grapes. That means that is the dependent variable. The number of grapes depends on the number of branches. In example 2, what is the input and what is the output? A farmer puts cows in his barn and gets out milk. The cows are the input meaning that is the independent variable. The milk is the output meaning that is the dependent variable. In example 3, what is the input and what is the output? What do we really want to know? The final cost. However, to find the cost we first have to know how many months you are going to be a member. That means that 66
2 the number of months is the input, or independent variable. Once we input the number months into the rule (which happens to be times 15 and then plus 20), we output the cost, which is the dependent variable. In the standard equation form of a linear function,, what is the input and output? Since we re talking about and on the coordinate plane, those are my input and output, but which is which? Generally speaking, but not always, the output is the variable by itself in any equation. In particular, in our generic form linear function, the variable is the output. That makes the input. If we plug in (input) an value then we get out (output) a value. Slope or Let s look at our examples again. Example 1 The number of grapes depends on the number of branches off the main vine and is represented by this equation: Example 2 A dairy farmer can produce 25 gallons of milk from 3 cows Example 3 The cost for joining a gym includes a start up fee plus dues every month In example one, the rate of change is given in the equation as the slope, or in the equation. Note that the slope is 100 which means that the rate of change is also 100, or in fraction form. This means that 100 grapes grow for every one branch. Months Perhaps it is easiest to see the rate of change (or slope) in the second example. How does the amount of milk change for the farmer? He gets 25 more gallons of milk for every 3 more cows he has, so we would write that rate of change as. In the third example, we ll need to find the slope by counting the rise and run. This is easiest to do from the intercept, the point where the line crosses the axis. Notice that the line crosses the axis at 20. The next nice point is at 1, 30. To get to that point from the intercept, you have to go up ten and right one. That means the slope, or rate of change, is 10. This means that the gym charges 10 dollars for every one month of membership. Cost in $ 67
3 Intercept or Let s look at our examples one last time. Example 1 Example 2 Example 3 The number of grapes depends on the number of branches off the main vine and is represented by this equation: A dairy farmer can produce 25 gallons of milk from 3 cows The cost for joining a gym includes a start up fee plus dues every month In example one, the initial is given in the equation as the intercept, or value in. Note that the initial value is 4. This means that only 4 grapes grow off the main vine no matter how many branches come off the main vine. Months The second example may be confusing because it s hard to see an initial value. An initial value would mean the amount of milk that the farmer starts with. Well, without any cows he wouldn t have any milk, so the initial value is 0. That s why there is no other number mentioned. We previously found the intercept for the third example to be 20. That means that no matter how many months you pay for membership to the gym, there will always be an additional $20 fee to pay. The problem context describes it as a start up fee. So if you pay for 3 months membership, you ll pay the $20 fee on top of the price per month. If you pay for 85 months of membership, you ll still pay the same $20 fee on top of the price per month. Cost in $ The Equation of the Line Once you know all the pieces, it s simply a matter of putting them in the right order. Since every linear function can be written in the form of, put the equation in that form. Remember that is the dependent variable (output), is the independent variable (input), is the rate of change (slope), and is the initial value ( intercept). For Example 2, we know that gallons of milk depends on the cows, the rate of change is, and the initial value is 0. Therefore, the equation is:. For Example 3, we know that the cost depends on the number of months you sign up for membership at the gym, the rate of change is 10, and the initial value is 20. Therefore, the equation is:
4 Lesson 2.2 Identify the rate of change, initial value, independent variable, and dependent variable. Then describe what the rate of change and initial value mean in the context of each situation. Finally, write the equation of the linear function. 1. A 2.5 foot rocket s distance traveled in meters based on time in seconds is modeled by the following function: 5 2. : : Cost in $ 2. The cost for 6 people to travel in a taxi in New York based on the number of miles driven is shown by the following graph: : : Miles driven 3. Planet Wiener receives $2.25 for every hotdog sold. They spend $105 for 25 packages of hot dogs and 10 packages of buns. Think of the linear function that demonstrates the profit based on the number of hotdogs sold. : : 69
5 4. The weight (in pounds) of a 20 x 10 x 12 aquarium tank based on the number of gallons of water inside is modeled by the following function: : : Profit 5. The amount of profit of the lemonade stand on 120 W Main Street based on the number of glasses of lemonade sold is modeled by the following graph: : : # of glasses sold 6. A candle starts at a height of 5 inches and diameter of 3 inches and burns 1 inch every 2 hours. Think of the linear function that demonstrates the height of the candle in terms of the time it has been burning. : : 70
6 7. The cost to stay in a 4 star hotel each night is modeled by the following function: _ : : 8. The cost to attend a sports clinic 37 miles away based on the number of days attended is modeled by the following graph: _ Cost : : Days 9. A dog kennel charges $40 for each night the dog stays in the kennel. Each day includes a 2 hour play time and 1 hour etiquette training. The kennel also charges a $10 bathing fee for a bath before the dog returns home. Think of the linear function that demonstrates the cost of putting a dog in the kennel in terms of the number of nights. _ : : 71
7 10. The number of gallons of gas in your 15 gallon gas tank based on the number of miles traveled is modeled y the following function: 12. _ : : 11. The number of pizzas ordered for 8 th grade night based on the number of students is shown by the following graph: Number of pizzas : : Number of students 12. It costs $5.50 to mail a large package to New Zealand. The post office will weigh your package and charge you an extra $0.30 per pound. The delivery takes 2 weeks. Think of the linear function that demonstrates the cost to mail a large package to New Zealand based on the number pounds it weighs. : : 72
8 13. An author wrote an 876 page book. The amount of profit based on the number books sold is modeled by the following function: _ : : Grade earned 14. The average grade earned on the Unit 3 test based on the number of hours of studying is modeled by the following graph: _ : : EQ of Line: Hours of studying 15. Kiley invited 32 people to her 13 th birthday party at the bowling alley. She hopes most people can come! It costs $40 to reserve the bowling alley. It will cost an additional $2 per friend to bowl. Think of the linear function that demonstrates the cost of the birthday party in terms of the number of friends who attend and bowl. : : 73
9 16. You started a mowing business so you could buy a 2015 Chevy Camaro when you turn 16. The amount of money in your bank account based on the number of yards you mow is modeled by the following function: 30. : : Temperature 17. When an oven is set at 350, the internal temperature of a chicken breast after every minute it s in the oven is modeled by the following graph: _ : : EQ of Line: Minutes 18. Walter s Water Adventures charges $34 to enter. This fee helps pay for maintenance and lifeguards. They always have 3 lifeguards at each slide plus 2 watching the wave pool. Think of the linear function that demonstrates the number of lifeguards on duty based on the number of slides open on a given day. : : 74
Lesson 2.6 Creating and Graphing Linear Equations in Two Variables
Lesson 2.6 Creating and Graphing Linear Equations in Two Variables Concept: Graphing Linear Equations EQ: How do I create and graph a linear equation in two variables from a word problem? (Standard CED.2)
More informationFinding the Equation from a Slope and y-intercept
Lesson 4.4 Objectives Write linear equations given a slope and y-intercept, a slope and a point, or a graph. Writing Linear Equations Michael turns on the high-temperature oven each morning when he comes
More informationLesson 31: Problems in Mathematical Terms
Lesson 31: Problems in Mathematical Terms Classwork Example 1 Marcus reads for 30 minutes each night. He wants to determine the total number of minutes he will read over the course of a month. He wrote
More informationSummer Math Packet for Entering Algebra 1 Honors Baker High School
Summer Math Packet for Entering Algebra 1 Honors Baker High School *You should be fluent in operations with fractions involved (multiplying, dividing, adding, and subtracting). *You should know all of
More informationLinear functions Increasing Linear Functions. Decreasing Linear Functions
3.5 Increasing, Decreasing, Max, and Min So far we have been describing graphs using quantitative information. That s just a fancy way to say that we ve been using numbers. Specifically, we have described
More informationAlgebra I EOC - Review 1 st Semester, (2x + 1) 3
Algebra I EOC - Review 1 st Semester, 2013 Simplify the following. 1. - 2 1 (x 3) + 5 4 (2x + 1) 2. 4 3 (2x + 1) 3 2 (x 1) 3. (6x 4) + 5(2x + 3) 4. -2(3x 1) 4(x + 1) Find the following for each of the
More informationESSENTIAL QUESTION How do you find a rate of change or a slope? Day 3. Input variable: number of lawns Output variable:amount earned.
L E S S O N 3.2 Rate of Change and Slope 8.F.4 Determine the rate of change of the function from two (x, y) values, including reading these from a table or from a graph. ESSENTIAL QUESTION How do you find
More informationGrade 7: Chapter 1 Practice Test & Vocabulary Review
Name: Date: Class: Grade 7: Chapter 1 Practice Test & Vocabulary Review 1) Find the unit rate: breaks in hours 2) Find the unit price: for CDs 3) During Tracy s trip across the country, she traveled 2,884
More information1) ordered pair: 2) function: 3) domain: 4) range: 5) solution of a linear equation: 6) proportional graph: 7) origin: 8) slope: 9) rise: 10) run:
ARE YOU READY? 7 th Grade Accelerated Chapter 11 Name: Vocabulary Date: Block: Write the definition for the following terms. Give an example if possible. 1) ordered pair: 2) function: 3) domain: 4) range:
More informationA. Linear B. Quadratic C. Cubic D. Absolute Value E. Exponential F. Inverse G. Square Root
UCS JH Algebra I REVIEW GD #2 1 Which family of function does each graph belong? A. Linear B. Quadratic C. Cubic D. Absolute Value E. Exponential F. Inverse G. Square Root 2 The coach of a basketball team
More information2015 Algebra 1 Semester Exam Review. Write an equation to represent the graph below. Which ray on the graph best represents a slope of 55 mph?
2015 Algebra 1 Semester Exam Review 1. Write an equation to represent the graph below. 2. 2. In the distance formula d = rt, r represents the rate of change, or slope. Which ray on the graph best represents
More informationName Date Period. Interpreting the Effects of Changing Slope and Y-intercept (6f) Slope tells you: Y-intercept tells you:
Name Date Period Interpreting the Effects of Changing Slope and Y-intercept (6f) Slope tells you: Y-intercept tells you: Example: Sam works as a bicycle courier. She earns $10.00 for each delivery plus
More informationKDS Grade 7 Math Comprehensive Assessment SBAC Assessment ID: dna ib
1 Select the two tables that represent a proportional relationship between x and y. A. x 2 1 0 1 y 4 2 0 2 B. x 0 1 2 3 y 5 8 11 14 C. x 3 5 7 9 y 21 35 49 63 D. x 0 2 4 6 y 0 12 20 28 2 1 Timmy uses 1
More informationSJAM MPM 1D Unit 5 Day 13
Homework 1. Identify the dependent variable. a) The distance a person walks depends on the time they walk. b) The recipe for 1 muffins requires cups of flour. c) Houses need 1 fire alarm per floor.. Identify
More informationRepresenting Linear Functions. Constant Rate of Change and Direct Variation. Writing Linear Equations
Lesson 7-1 Lesson 7-2 Lesson 7-3 Lesson 7-4 Lesson 7-5 Lesson 7-6 Lesson 7-7 Lesson 7-8 Functions Representing Linear Functions Rate of Change Constant Rate of Change and Direct Variation Slope Slope-Intercept
More informationnotebook October 08, What are the x and y intercepts? (write your answers as coordinates).
3.4 Opening Activity: Draw a graph of the equation y = 5x + 20 What are the x and y intercepts? (write your answers as coordinates). How are you able to use the equation but NOT the graph to find the x
More informationLesson 8: Systems of Inequalities Word Problems
Lesson 8: Systems of Inequalities Word Problems Example 1 The girls swim team is hosting a fund raiser. They would like to raise at least $500. They are selling candles for $5 and flower arrangements for
More information(GPA, student) (area code, person) (person, shirt color)
Foundations of Algebra Unit 5 Review Part One Name: Day One: Function Notation In order for a relation to be a function, every must have exactly one. 1) Determine whether each of the following represents
More informationDecimal Multiplication and Division 1) ) ) ) ) 5.4 x ) x 2
Level B2 Review Packet This packet briefly reviews the topics covered on the Level A Math Skills Assessment. If you need additional study resources and/or assistance with any of the topics below, please
More informationcar, in years 0 (new car)
Chapter 2.4: Applications of Linear Equations In this section, we discuss applications of linear equations how we can use linear equations to model situations in our lives. We already saw some examples
More informationMod 3 Word Problems #1 CW/HW
Name KEY Math 075 Mod 3 Word Problems #1 CW/HW 1. Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Find the slope, including units, and write a
More information3 Ways to Write Ratios
RATIO & PROPORTION Sec 1. Defining Ratio & Proportion A RATIO is a comparison between two quantities. We use ratios everyday; one Pepsi costs 50 cents describes a ratio. On a map, the legend might tell
More information4.5 Comparing Exponential Functions
4.5 Comparing Exponential Functions So far we have talked in detail about both linear and exponential functions. In this section we ll compare exponential functions to other exponential functions and also
More informationIn a moment, we will look at a simple example involving the function f(x) = 100 x
Rates of Change Calculus is the study of the way that functions change. There are two types of rates of change: 1. Average rate of change. Instantaneous rate of change In a moment, we will look at a simple
More informationWhat is the slope of the line? What does the slope represent in the context of the problem?
Desk 1 Ismael started the day with an irrigation pipe 120 feet long. He used the equation L = 15s + 120 to determine the total length of the pipe as new sections of pipe, s, were welded on to the end.
More informationAnalyzing Linear Graphs Application Practice
Algebra 1 Name: Date: Class#: Analyzing Linear Graphs Application Practice 1) The equation y = 5x + 50 represents your elevation y in feet for each minute x you hike from a trailhead. b) Graph the equation
More informationTCM Final Review Packet Name Per.
TCM Final Review Packet Name Per. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Translate the statement into a formula. 1) The total distance traveled,
More informationUnit 10 Independent Summer Packet
Unit 10 Independent Summer Packet Name For each skill in this packet, there are examples, explanations and definitions to read followed by practice problems for you to complete. Complex Fractions and Unit
More informationHonors Midterm Study Guide
Name Date Unit 1: Rational Numbers (No Calculator) Honors Midterm Study Guide Classify each number below. Use a check to indicate if a number is part of a given category. Leave the space blank if it does
More informationNorth Carolina READY End-of-Grade Assessment Mathematics RELEASED. Grade 5. Student Booklet
REVISE 7//0 Released Form North arolina REY End-of-Grade ssessment Mathematics Grade Student ooklet cademic Services and Instructional Support ivision of ccountability Services opyright 0 by the North
More informationMathematics Success Grade 8
Mathematics Success Grade 8 T379 [OBJECTIVE] The student will derive the equation of a line and use this form to identify the slope and y-intercept of an equation. [PREREQUISITE SKILLS] Slope [MATERIALS]
More information3 Ways to Write Ratios
RATIO & PROPORTION Sec 1. Defining Ratio & Proportion A RATIO is a comparison between two quantities. We use ratios every day; one Pepsi costs 50 cents describes a ratio. On a map, the legend might tell
More information3 Ways to Write Ratios
RATIO & PROPORTION Sec 1. Defining Ratio & Proportion A RATIO is a comparison between two quantities. We use ratios every day; one Pepsi costs 50 cents describes a ratio. On a map, the legend might tell
More information(To be administered after NPS Grade 7 Scope and Sequence Units 3&4) Assessed Standards: 7.RP.1 7.RP.2 7.RP.3 7.EE.3
ADAPTED NJDOE ASSESSMENT GRADE 7 (To be administered after NPS Grade 7 Scope and Sequence Units 3&4) Assessed Standards: 7.RP. 7.RP. 7.RP.3 7.EE.3 [Type text] The Newark Public Schools - Office of Mathematics
More informationP.O.D. Wrap Up. Independent and Dependent Variables
Wrap Up Independent and Dependent Variables P.O.D. 1. Simplify this math sentence: (x+2)+(2x-5) 2. Graph the following: x 27 3. Simplify the following: a) 4(x + 7) b) 3(4 + 9) c) x(4 + 9) Tuesday, March
More information3. Joyce needs to gather data that can be modeled with a linear function. Which situation would give Joyce the data she needs?
Unit 6 Assessment: Linear Models and Tables Assessment 8 th Grade Math 1. Which equation describes the line through points A and B? A. x 3y = -5 B. x + 3y = -5 C. x + 3y = 7 D. 3x + y = 5 2. The table
More information35 38 point slope day 2.notebook February 26, a) Write an equation in point slope form of the line.
LT 6: I can write and graph equations in point slope form. p.35 What is point slope form? What is slope intercept form? Let's Practice: There is a line that passes through the point (4, 3) and has a slope
More informationLinear Modeling Business 5 Supply and Demand
Linear Modeling Business 5 Supply and Demand Supply and demand is a fundamental concept in business. Demand looks at the Quantity (Q) of a product that will be sold with respect to the Price (P) the product
More informationSection 4.3 Objectives
CHAPTER ~ Linear Equations in Two Variables Section Equation of a Line Section Objectives Write the equation of a line given its graph Write the equation of a line given its slope and y-intercept Write
More informationNOTES ON CALCULUS AND UTILITY FUNCTIONS
DUSP 11.203 Frank Levy Microeconomics Tutorial 1 NOTES ON CALCULUS AND UTILITY FUNCTIONS These notes have three purposes: 1) To explain why some simple calculus formulae are useful in understanding utility
More informationComplete each table. Then, sketch a graph that represents the problem situation.
Lesson.1 Skills Practice Name Date I Graph in Pieces Linear Piecewise Functions Problem Set Complete each table. Then, sketch a graph that represents the problem situation. 1. Rosa saved $100 to spend
More informationWeek #4: Review of The Heart of Algebra
Week #4: Review of The Heart of Algebra 1. Which of the following best describes the solutions to the inequality 3l 6 8? A) l K L B) l 2 C) l PQ L D) l 14 2. In the equation, 3 + 10x 5 = a + 1 x 2, a is
More informationSUMMER MATH PACKET 1-b
SUMMER MATH PACKET 1-b The problems in this packet have been selected to help you to review concepts in preparation for your next math class. Please complete the odd problems in this packet. Show your
More informationSection 7C Finding the Equation of a Line
Section 7C Finding the Equation of a Line When we discover a linear relationship between two variables, we often try to discover a formula that relates the two variables and allows us to use one variable
More informationBARUCH COLLEGE MATH 2003 SPRING 2006 MANUAL FOR THE UNIFORM FINAL EXAMINATION
BARUCH COLLEGE MATH 003 SPRING 006 MANUAL FOR THE UNIFORM FINAL EXAMINATION The final examination for Math 003 will consist of two parts. Part I: Part II: This part will consist of 5 questions similar
More informationInterpreting the Unit Rate as Slope
L E S S N 3.3 Florida Standards The student is expected to: Expressions and Equations.EE.. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different
More informationA C E. Answers Investigation 4. Applications. x y y
Answers Applications 1. a. No; 2 5 = 0.4, which is less than 0.45. c. Answers will vary. Sample answer: 12. slope = 3; y-intercept can be found by counting back in the table: (0, 5); equation: y = 3x 5
More informationModeling Relationships. 2. What is a linear function? How can you determine if a function is linear or not?
Modeling Relationships 1. What is a function? 2. What is a linear function? How can you determine if a function is linear or not? 3. How can you determine the rate of change given the equation of a linear
More informationCH 3 P4 as of ink
1 2 3 4 5 Ron has a player s card for the arcade at the mall. His player s card keeps track of the number of credits he earns as he wins games. Each winning game earns the same number of credits, and those
More informationAlgebra Success. LESSON 14: Discovering y = mx + b
T282 Algebra Success [OBJECTIVE] The student will determine the slope and y-intercept of a line by examining the equation for the line written in slope-intercept form. [MATERIALS] Student pages S7 S Transparencies
More informationExtra Practice Chapter 6
Extra Practice Chapter 6 Topics Include: Equation of a Line y = mx + b & Ax + By + C = 0 Graphing from Equations Parallel & Perpendicular Find an Equation given Solving Systems of Equations 6. - Practice:
More informationMA-1. North Carolina Math 1 Unit 2 Mid-Unit Assessment. Name: Class: Date:
Name: Class: _ Date: _ North Carolina Math 1 Unit 2 Mid-Unit Assessment Multiple Choice Identify the choice that best completes the statement or answers the question. 1. It costs $125 to buy a heater and
More informationSPIRIT 2.0 Lesson: Am I Straight?
SPIRIT 2.0 Lesson: Am I Straight? ===============================Lesson Header ============================== Lesson Title: Am I Straight? Draft Date: July 21, 2008 1st Author (Writer): Neil Hammond 2nd
More informationRatios and Proportions. Fraction/Decimal/Percent Conversions Ratios Rates/ Unit Rates Proportions Percent Application Measurement Conversions
Ratios and Proportions Fraction/Decimal/Percent Conversions Ratios Rates/ Unit Rates Proportions Percent Application Measurement Conversions Fill in the missing pieces in charts below. Fraction Decimal
More informationModule 2- A Coordinate Geometry. 1. What is an equation of the line whose graph is shown? A. y = x B. y = 2x C. y = x D.
Name: Date: 1. What is an equation of the line whose graph is shown? A. y = x B. y = 2x C. y = x D. y = 2 2. Which is an equation for line l in the accompanying diagram? A. y = 2x + 2 B. y = 2x 4 C. y
More informationList the quadrant(s) in which the given point is located. 1) (-10, 0) A) On an axis B) II C) IV D) III
MTH 55 Chapter 2 HW List the quadrant(s) in which the given point is located. 1) (-10, 0) 1) A) On an axis B) II C) IV D) III 2) The first coordinate is positive. 2) A) I, IV B) I, II C) III, IV D) II,
More informationExploring Slope. High Ratio Mountain Lesson 11-1 Linear Equations and Slope
Eploring Slope High Ratio Mountain Lesson 11-1 Learning Targets: Understand the concept of slope as the ratio points on a line. between any two Graph proportional relationships; interpret the slope and
More informationReview Problems for MAT141 Final Exam
Review Problems for MAT141 Final Exam The following problems will help you prepare for the final exam. Answers to all problems are at the end of the review packet. 1. Find the area and perimeter of the
More information5.2E Lesson: Proportions in Tables and Graphs*
5.2E Lesson: Proportions in Tables and Graphs* Name: Period: 1. Use Graph A below to fill in the table relating calories to snacks. Number Number of Ordered Write a complete sentence describing the meaning
More informationEOC Review Days 2 & 3: Linear Basics, Slope, and Intercepts
Name: Date: Period: Algebra 1 Bowling, Cawthon, Fletcher, Skiles EOC Review Days 2 & 3: Linear Basics, Slope, and Intercepts 1. Find the x-intercept and the y-intercept for the function represented in
More informationTrimester 2 Final Practice CC 7 Date Period. Unit Rates (7.RP.1)
Trimester 2 Final Practice Name CC 7 Date Period Unit Rates (7.RP.1) 1. This diagram shows how much apple juice is mixed with carrot juice for a recipe. How many cups of apple juice are used for 1 cup
More informationRevision G6. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What percent of the figure is shaded?
Revision G6 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What percent of the figure is shaded? a. % b. 3% c. 30% d. 300% 2. The town garden has 80%
More informationPlease show work for all calculated answers. Show work in a neat and organized manner.
Math 083 Review for Final Exam Name Please show work for all calculated answers. Show work in a neat and organized manner. 1) Using the frequency table for a monthly budget, find all of the relative frequencies
More informationEconomics 101 Fall 2016 Answers to Homework #1 Due Thursday, September 29, 2016
Economics 101 Fall 2016 Answers to Homework #1 Due Thursday, September 29, 2016 Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number
More informationReview Exercise Set 13. Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such.
Review Exercise Set 13 Exercise 1: Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such. Exercise 2: Write a linear function that can
More informationMathematics Success Level H
Mathematics Success Level H T473 [OBJECTIVE] The student will graph a line given the slope and y-intercept. [MATERIALS] Student pages S160 S169 Transparencies T484, T486, T488, T490, T492, T494, T496 Wall-size
More information1. Amy baby-sat from 7:30 p.m. to 11:00 p.m. If Amy was paid $15.75, how much did she earn per hour?
Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 07 Mathematics Mathematics Exam 1 Description: 7th Grade Regular Topic I Assessment - Mathematics Form: 201 Assessment
More informationPractice 5-4. Unit Rates and Slope. Name Class Date
Name Class Date Practice 5-4 Unit Rates and Slope 5-4 Unit Rates and Slope 1. The graph shows the number of centimeters a particular plant grows over time. Given the points (0,0) and (4,6), how many centimeters
More information4.1 Write Linear Equations by Using a Tables of Values
4.1 Write Linear Equations by Using a Tables of Values Review: Write y = mx + b by finding the slope and y-intercept m = b = y = x + Every time x changes units, y changes units m = b = y = x + Every time
More information4. a. This table shows two points that are on the same straight line. Complete the table to show three other points on the same line.
Moving Straight Ahead Study Questions 0. Sharon owns a bakery that makes cakes. She must pay a monthly rent for the bakery, and has to pay for ingredients for each cake. In January she made 300 cakes and
More informationHandout to accompany Worksheet #1
Handout to accompany Worksheet #1 Situation: The graph below is distance vs. time for a rocket car traveling on the rocket car freeway. 6 5 4 distance 3 (in miles) 2 1 1 2 3 4 5 6 7 time (in minutes) 1
More informationClasswork. Opening Exercise. Example 1
Classwork Opening Exercise Xin is buying beverages for a party, which are individually packaged and come in packs of 8. Let be the number of packages Xin buys and be the total number of beverages. The
More informationShow your work. Write your answer on the line to the right. 1. Solve. Show your work. 1. EE.7
Name Date 8th Grade Semester 2 Assessment Standard Show your work. Write your answer on the line to the right. 1. Solve. Show your work. 1. EE.7 2. Solve. Show your work. 2. EE.7 EE.7.b 2z + 3 + 7z = 12
More informationContents. Solving Real-World Problems with Ratios and Percents Using Proportional Relationships to Solve Multi-Step Problems
Contents New York State Common Core Learning Standards for Mathematics Lesson Computing Unit Rates... Lesson Identifying the Constant of Proportionality... 7.RP. 7.RP..b Lesson Lesson Solving Real-World
More informationUnit 3: Writing Equations Chapter Review
Unit 3: Writing Equations Chapter Review Part 1: Writing Equations in Slope Intercept Form. (Lesson 1) 1. Write an equation that represents the line on the graph. 2. Write an equation that has a slope
More informationTABLE OF CONTENTS. About Finish Line PA Core Math 5. UNIT 1: Big Ideas from Grade 5 7 UNIT 1 REVIEW 39
TABLE OF CONTENTS About Finish Line PA Core Math 5 UNIT 1: Big Ideas from Grade 5 7 LESSON 1 CC.2.1.5.C.2 Multiplying Fractions [connects to CC.2.3.6.A.1] 8 LESSON 2 CC.2.1.5.B.2 Operations with Decimals
More informationWriting Linear Equations from a Context
Writing Linear Equations from a Context Word problems in Slope-intercept form When a word problem involves a constant rate or speed and a beginning amount, it can be written in slope-intercept form: y
More informationb) According to the statistics above the graph, the slope is What are the units and meaning of this value?
! Name: Date: Hr: LINEAR MODELS Writing Motion Equations 1) Answer the following questions using the position vs. time graph of a runner in a race shown below. Be sure to show all work (formula, substitution,
More informationDiscrete & Continuous Domains
Discrete & Continuous Domains 1 Functions shows a recipes mix of adult & children show tickets. Domain (x values): 0, 1, 2, 3, 4 Range (y values): 8, 6, 4, 2, 0 The domain is discrete because it has only
More informationpar ( 12). His closest competitor, Ernie Els, finished 3 strokes over par (+3). What was the margin of victory?
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) Tiger Woods won the 2000 U.S. Open golf tournament with a score of 2 strokes under par
More informationLesson 12 Section 2.3
Lesson Section.3 Compare the graphs of the lines below. A B C = = + 3 = - 4 0 0 0 3 0-4 - - - - -6 4 7 0-3 -6-3 -3-3 0 How does each point of graph B compare with graph A (directl below)? How does each
More informationLesson 10: Interpreting Quadratic Functions from Graphs and Tables
: Interpreting Quadratic Functions from Graphs and Tables Student Outcomes Students interpret quadratic functions from graphs and tables: zeros ( intercepts), intercept, the minimum or maximum value (vertex),
More informationChapter 6 BLM Answers
Chapter 6 BLM Answers BLM 6 2 Chapter 6 Prerequisite Skills 1. a) 0.50, 50% 0.60, 60% 2.3, 233.3% d) 3, 300% 108 km/h 160 m/km 50 m/min 3. 1.99 m 4. a) Time Worked, t (h) Earnings, E ($) 2 30 4 60 6 90
More informationdollars per person; the cost is $45 for each person. dollars per person; the cost is $1 for 225 people.
Name: ate: 1 The table shows the cost of a vacation package for a given number of people. The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for
More informationFINITE MATH LECTURE NOTES. c Janice Epstein 1998, 1999, 2000 All rights reserved.
FINITE MATH LECTURE NOTES c Janice Epstein 1998, 1999, 2000 All rights reserved. August 27, 2001 Chapter 1 Straight Lines and Linear Functions In this chapter we will learn about lines - how to draw them
More informationStart. Finish. Rational Race. Go back. Move ahead 1 and go again. Classroom Strategies Blackline Master I - 31 Page 73
Finish Start Rational Race Go back Move ahead and go again 4 2 Classroom Strategies Blackline Master I - Page 7 / of 24 / 5 + 4 / 5 / 5 5 / 7 8 0% of 75 2 / 5 / 2 of 2 / 5 / 7 6.4 7.5 / 5 40.2 4 2 / of
More informationMFM 1P. Foundations of Mathematics Grade 9 Applied Mitchell District High School. Unit 2 Proportional Reasoning 9 Video Lessons
MFM 1P Foundations of Mathematics Grade 9 Applied Mitchell District High School Unit 2 Proportional Reasoning 9 Video Lessons Allow no more than 14 class days for this unit! This includes time for review
More informationMath Fundamentals for Statistics (Math 52) Homework Unit 6: Rates/Ratios/Proportions. Scott Fallstrom and Brent Pickett The How and Whys Guys
Math Fundamentals for Statistics (Math 52) Homework Unit 6: Rates/Ratios/Proportions Scott Fallstrom and Brent Pickett The How and Whys Guys Homework Unit 6 Page 1 6.1: Comparing Objects Ratios and Rates
More informationGRAPHS AND EXAMPLES FOR LECTURE MATH 111
GRAPHS AND EXAMPLES FOR LECTURE MATH 111 Lecture Materials for Supplement Sections 1 and 2 Situation: This is the graph of distance traveled for a car driving on a long straight road. 550 500 450 400 distance
More informationName: Class: Date: in general form.
Write the equation in general form. Mathematical Applications for the Management Life and Social Sciences 11th Edition Harshbarger TEST BANK Full clear download at: https://testbankreal.com/download/mathematical-applications-management-life-socialsciences-11th-edition-harshbarger-test-bank/
More informationMAT Pre-Calculus Class Worksheet - Word Problems Chapter 1
MAT 111 - Pre-Calculus Name Class Worksheet - Word Problems Chapter 1 1. The cost of a Frigbox refrigerator is $950, and it depreciates $50 each year. The cost of a new Arctic Air refrigerator is $1200,
More informationSemester Exam Review
Semester Exam Review Name Date Block MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the given equation, find the values of a, b, and c, determine
More informationAcc. Alg. II W.S. Sec Assign. # 5. Show work to justify all answers!!!!!!!
Acc. Alg. II W.S. Sec. 1.1-1.4 Assign. # 5 Name Show work to justify all answers!!!!!!! 1. Determine p so that the slope of the line containing this pair of points has the given value. 5 ( -2, p), (4,
More informationUnit 8 - Math Review. Section 8: Real Estate Math Review. Reading Assignments (please note which version of the text you are using)
Unit 8 - Math Review Unit Outline Using a Simple Calculator Math Refresher Fractions, Decimals, and Percentages Percentage Problems Commission Problems Loan Problems Straight-Line Appreciation/Depreciation
More informationPractice Problem Solutions for Exam 1
p. 1 of 17 ractice roblem olutions for Exam 1 1. Use a supply and demand diagram to analyze each of the following scenarios. Explain briefly. Be sure to show how both the equilibrium price and quantity
More informationEXAMPLE 2 COMMON CORE
REFLECT. Why can it be helpful to solve a linear equation for y? Graphing a Linear Function Using the Slope and y-intercept You can graph the linear function f() = m + b using only the slope m and y-intercept
More informationLesson 3.3 Constant Rate of Change (linear functions)
Lesson 3.3 Constant Rate of Change (linear functions) Concept: Characteristics of a function EQ: How do we analyze a real world scenario to interpret a constant rate of change? (F.IF.7) Vocabulary: Rate
More informationEquations. Krista Hauri I2T2 Project
Applied Linear Equations Krista Hauri I2T2 Project Grade Level: 9 th Intergraded Algebra 1 Time Span : 5 (40 minute) days Tools: Calculator Base Ranger (CBR) at least 4 TI-84 Graphing Calculator for each
More informationPlanning a Road Trip: Trip Planner
7 th Grade Math Name Unit 2 Proportional Relationships Date Homeroom Planning a Road Trip: Trip Planner For your final project, you will take on the role of a student planning a summer road trip for you
More informationLesson 5: Identifying Proportional and Non-Proportional Relationships in Tables Bellringer
Lesson 5: Identifying Proportional and Non-Proportional Relationships in Tables Bellringer 1) What is the greatest common factor of 132 and 77? a. 1 b. 7 c. 11 d. 12 2) Nick can run 9.3 miles in a. 3.1
More information