Chapter 3: Linear Functions

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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217 3 Linear Functions In this chapter we will study a class of function called a linear function , so named because the graph of a linear function is a line. We begin our study of linear functions by examining some linear models, where we will present a thorough discussion of the modeling process, including the notion of dependent and independent variables, and representing the data with a graph, properly labeled and scaled. We will learn that if one quantity changes at constant rate with respect to a second quantity, the functional relationship must be linear and the graph will be a line. We will also learn how to develop model equations, then use both the model equation and the graph to make predictions. We will then present a discussion on slope, making the connection to the constant rates provided in the linear models section previously studied. From there we move to a more formal definition of the slope of a line, a number that controls the “steepness” of the line. We conclude the chapter with a discussion of the equation of a linear function, using two important forms: the slope-intercept form and point-slope form . Finally, we will use these forms to determine a “line of best fit” for a variety of data sets. Welcome to the world of linear models. Let’s begin. Table of Contents 3.1 Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Modeling the Discrete with the Continuous 224 Determining the Equation Model from the Graph 228 Exercises 233 Answers 244 3.2 Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 The Slope Formula 251 Parallel Lines 256 Perpendicular Lines 258 Exercises 261 Answers 267 3.3 Equations of Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 The Slope-Intercept Form 271 Making Connections 275 The Standard Form of a Line 276 Intercepts 278 Horizontal and Vertical Lines 280 Exercises 283 Answers 289 3.4 The Point-Slope Form of a Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 Parallel Lines 297 Perpendicular Lines 299
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218 Chapter 3 Linear Functions Version: Fall 2007 Applications of Linear Functions 301 Exercises 305 Answers 309 3.5 The Line of Best Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 Using the Graphing Calculator to Find the Line of Best Fit 316 Exercises 321 Answers 327 3.6 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Copyright All parts of this intermediate algebra textbook are copyrighted in the name of Department of Mathematics, College of the Redwoods. They are not in the public domain. However, they are being made available free for use in educational in- stitutions. This offer does not extend to any application that is made for profit. Users who have such applications in mind should contact David Arnold at david- [email protected] or Bruce Wagner at [email protected] This work (including all text, Portable Document Format files, and any other orig- inal works), except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License, and is copyrighted C 2006, Department of Mathematics, College of the Redwoods. To view a copy of this license, visit or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA.
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Section 3.1 Linear Models 219 Version: Fall 2007 3.1 Linear Models
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