MAHS-DV Algebra 1-2 Q2

MAHS-DV Algebra 1-2 Q2 Adrienne Wooten Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) www.ck12.org AUTHOR Adrienne Wooten To access a customizable version of this book, as well as other interactive content, visit www.ck12.org CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook®, CK-12 intends to pioneer the generation and distribution of high-quality educational content that will serve both as core text as well as provide an adaptive environment for learning, powered through the FlexBook Platform®. 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Printed: October 7, 2013 iii Contents www.ck12.org Contents 1 Modeling Linear Data 1 1.1 Line Graphs............................................. 2 1.2 Scatter Plots............................................. 8 1.3 Scatter Plots and Linear Correlation ................................ 16 1.4 Linear Regression Equations .................................... 24 1.5 Least-Squares Regression...................................... 31 2 Statistics 40 2.1 Measures of Central Tendency ................................... 41 2.2 Measures of Dispersion....................................... 49 2.3 Displaying Univariate Data..................................... 57 2.4 Histograms ............................................. 63 2.5 Box-and-Whisker Plots....................................... 75 2.6 Double Box-and-Whisker Plots................................... 83 2.7 Summarizing Categorical Data................................... 89 3 Linear Equations and Inequalities 93 3.1 Two-Step Equations and Properties of Equality........................... 94 3.2 Equations with Variables on Both Sides .............................. 99 3.3 Solving Multi-Step Equations....................................105 3.4 Solving Equations with Rational Numbers.............................110 3.5 Solving Algebraic Equations for a Variable.............................126 3.6 Compound Inequalities .......................................131 3.7 Applications with Inequalities....................................136 3.8 Graphing Linear Inequalities in Two Variables...........................140 4 Systems of Linear Equations and Inequalities 146 4.1 Graphs of Linear Systems......................................147 4.2 Solving Systems by Multiplying Both Equations to Cancel a Variable . 154 4.3 Solving Systems with One Solution Using Substitution ......................161 4.4 Systems of Linear Inequalities ...................................169 iv www.ck12.org Chapter 1. Modeling Linear Data CHAPTER 1 Modeling Linear Data Chapter Outline 1.1 LINE GRAPHS 1.2 SCATTER PLOTS 1.3 SCATTER PLOTS AND LINEAR CORRELATION 1.4 LINEAR REGRESSION EQUATIONS 1.5 LEAST-SQUARES REGRESSION 1 1.1. Line Graphs www.ck12.org 1.1 Line Graphs Here you’ll learn the difference between continuous data and discrete data as it applies to a line graph. You’ll also learn how to represent data that has a linear pattern on a graph and how to solve problems with line graphs. You’re scanning some photographs for a customer. The customer is charged a $25 set-up fee for the scanner and then 0.55 per scan. How much would the customer get charged for 8 scans? What about for 15 scans? Watch This First watch this video to learn about line graphs. MEDIA Click image to the left for more content. CK-12 Foundation: Chapter7LineGraphsA Then watch this video to see some examples. MEDIA Click image to the left for more content. CK-12 Foundation: Chapter7LineGraphsB Watch this video for more help. MEDIA Click image to the left for more content. Khan Academy Application problem with graph Guidance Before you continue to explore the concept of representing data graphically, it is very important to understand the meaning of some basic terms that will often be used in this concept. The first such definition is that of a variable. In statistics, a variable is simply a characteristic that is being studied. This characteristic assumes different values 2 www.ck12.org Chapter 1. Modeling Linear Data for different elements, or members, of the population, whether it is the entire population or a sample. The value of the variable is referred to as an observation, or a measurement. A collection of these observations of the variable is a data set. Variables can be quantitative or qualitative. A quantitative variable is one that can be measured numerically. Some examples of a quantitative variable are wages, prices, weights, numbers of vehicles, and numbers of goals. All of these examples can be expressed numerically. A quantitative variable can be classified as discrete or continuous. A discrete variable is one whose values are all countable and does not include any values between 2 consecutive values of a data set. An example of a discrete variable is the number of goals scored by a team during a hockey game. A continuous variable is one that can assume any countable value, as well as all the values between 2 consecutive numbers of a data set. An example of a continuous variable is the number of gallons of gasoline used during a trip to the beach. A qualitative variable is one that cannot be measured numerically but can be placed in a category. Some examples of a qualitative variable are months of the year, hair color, color of cars, a person’s status, and favorite vacation spots. The following flow chart should help you to better understand the above terms. Variables can also be classified as dependent or independent. When there is a linear relationship between 2 variables, the values of one variable depend upon the values of the other variable. In a linear relation, the values of y depend upon the values of x. Therefore, the dependent variable is represented by the values that are plotted on the y-axis, and the independent variable is represented by the values that are plotted on the x-axis. Example A Select the best descriptions for the following variables and indicate your selections by marking an ’x’ in the appropriate boxes. TABLE 1.1: Variable Quantitative Qualitative Discrete Continuous Number of members in a family A person’s marital status Length of a person’s arm 3 1.1. Line Graphs www.ck12.org TABLE 1.1: (continued) Variable Quantitative Qualitative Discrete Continuous Color of cars Number of errors on a math test The variables can be described as follows: TABLE 1.2: Variable Quantitative Qualitative Discrete Continuous Number of mem- x x bers in a family A person’s marital x status Length of a person’s x x arm Color of cars x Number of errors on x x a math test Example B Sally works at the local ballpark stadium selling lemonade. She is paid $15.00 each time she works, plus $0.75 for each glass of lemonade she sells. Create a table of values to represent Sally’s earnings if she sells 8 glasses of lemonade. Use this table of values to represent her earnings on a graph. The first step is to write an equation to represent her earnings and then to use this equation to create a table of values. y = 0:75x + 15, where y represents her earnings and x represents the number of glasses of lemonade she sells. TABLE 1.3: Number of Glasses of Lemonade Earnings 0 $15.00 1 $15.75 2 $16.50 3 $17.25 4 $18.00 5 $18.75 6 $19.50 7 $20.25 8 $21.00 4 www.ck12.org Chapter 1. Modeling Linear Data The dependent variable is the money earned, and the independent variable is the number of glasses of lemonade sold. Therefore, money is on the y-axis, and the number of glasses of lemonade is on the x-axis. From the table of values, Sally will earn $21.00 if she sells 8 glasses of lemonade. Now that the points have been plotted, the decision has to be made as to whether or not to join them. Between every 2 points plotted on the graph are an infinite number of values. If these values are meaningful to the problem, then the plotted points can be joined. This type of data is called continuous data. If the values between the 2 plotted points are not meaningful to the problem, then the points should not be joined. This type of data is called discrete data. Since glasses of lemonade are represented by whole numbers, and since fractions or decimals are not appropriate values, the points between 2 consecutive values are not meaningful in this problem. Therefore, the points should not be joined. The data is discrete. Guided Practice The local arena is trying to attract as many participants as possible to attend the community’s “Skate for Scoliosis” event. Participants pay a fee of $10.00 for registering, and, in addition, the arena will donate $3.00 for each hour a participant skates, up to a maximum of 6 hours. Create a table of values and draw a graph to represent a participant who skates for the entire 6 hours.

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