Module 4: Linear Functions (Chapter 4)
Section outline
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Imagine placing a plant in the ground one day and finding that it has doubled its height just a few days later. Although it may seem incredible, this can happen with certain types of bamboo species. These members of the grass family are the fastest-growing plants in the world. One species of bamboo has been observed to grow nearly 1.5 inches every hour (http://www.guinnessworldrecords.com/records-3000/fastest-growing-plant/). In a twenty-four hour period, this bamboo plant grows about 36 inches, or an incredible 3 feet! A constant rate of change, such as the growth cycle of this bamboo plant, is a linear function.
Recall from Functions and Function Notation (Section 3.2) that a function is a relation that assigns to every element in the domain exactly one element in the range. Linear functions are a specific type of function that can be used to model many real-world applications, such as plant growth over time. In this chapter, we will explore linear functions, their graphs, and how to relate them to data.
Image Caption: A bamboo forest in China (credit: "JFXie"/Flickr)
(Content & Image Source: Chapter 4 Introduction, Algebra and Trigonometry 2e, Jay Abramson, OpenStax, CC BY 4.0 License)
Upon completion of this module, you will be able to:Section 4.1 Linear Equations in Two VariablesSection 4.2 Linear Functions- Write an linear equation in two variables (CLO1)
- Given the equations of two lines, determine whether their graphs are parallel or perpendicular. (CLO1)
- Write the equation of a line parallel or perpendicular to a given line. (CLO1)
- Represent a linear function. (CLO1)
- Determine whether a linear function is increasing, decreasing, or constant.(CLO1)
- Interpret slope as a rate of change.(CLO1)
- Write and interpret an equation for a linear function.(CLO3)
- Graph linear functions.(CLO1)
Section 4.3 Modeling with Linear Functions
- Build linear models from verbal descriptions.(CLO3)
- Model a set of data with a linear function.(CLO3)
Section 4.4 Systems of Linear Equations: Two Variables
- Solve systems of equations by graphing. (CLO1, CLO3)
- Solve systems of equations by substitution.(CLO1, CLO3)
- Solve systems of equations by addition.(CLO1, CLO3)
- Identify inconsistent systems of equations containing two variables.(CLO1, CLO3)
- Express the solution of a system of dependent equations containing two variables.(CLO1, CLO3)
To achieve these objectives:- Read the Module 4 Introduction (see above).
- Read Sections 4.1 - 4.4 of Chapter 4: Linear Functions in College Algebra (links to each Section provided below)
- At the end of each Section there is a list of Key Concepts, Section Exercises, and a Glossary of terms
- At the end of each Section there is a list of Key Concepts, Section Exercises, and a Glossary of terms
- Complete the MyOpenMath Homework Assignments for each Section (links provided below) - These are graded!
- Practice the problems on the Chapter 4 Review Exercises, checking the solutions provided (link provided below)
- View the Chapter 4 Practice Test (link provided below)
- Complete the MyOpenMath Quiz for Chapter 4 (link provided below) - This is graded!
- Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
- Post in the Chapter 4 Q&A Discussion Forum - link provided below.
Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.Module Pressbooks Resources and Activities
You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.
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