Linear Equations

Learning Objectives Upon completion of this unit, students should be able to:

1. Identify the slope when given a linear equation or a graph of a line.

2. Find the slope and equation of a line when given two points.

3. Identify the slope and equation for horizontal and vertical lines.

4. Graph in, and interpret, slope-intercept form.

5. Compare the slopes of parallel and perpendicular lines.

6. Apply function notation and linear equations to evaluate business linear


7. Apply the echelon method to evaluate linear systems.

8. Identify and interpret types of solutions: no solution, unique solution, and

infinite number of solutions.

Written Lecture People learn in a variety of ways. For this reason, each section in each unit of this course will include multiple resources: required and supplemental readings assigned in the textbook, written notes for the student to access that provide additional examples of similar problem solutions, and video tutorials that demonstrate how to solve some of the problems in the notes. If pressed for time, the notes will give a detailed view of what is covered in each section. The best way to learn is by practicing. Each unit will not only provide instruction and guidance on how to solve problems, but also numerous opportunities to practice solving them on your own through non-graded Learning Activities. A Prerequisite Skills Diagnostic Test is provided on page xxiii of the textbook; you can use this test to determine if you need to refresh your memory on any of the mathematical skills needed for this course. Answers and guidance for solutions are provided in indicated sections of the textbook. Unit I introduces slopes and equations of lines and linear functions and their applications, as well as how to use the echelon method to solve linear systems. Section 1.1: Slopes and Equations of Lines We start with Section 1.1, which explores mathematics pertaining to linear models, using graphs with straight lines to plot data. This type of mathematical model has many uses. The information presented here will serve as a foundation for information in subsequent units, as well as in the rest of this unit. The Reading Assignment that aligns with this section of the unit is Section 1.1 (pp. 2-13) of the textbook. Videos that demonstrate examples of solutions used for slopes and line equations are provided. Make sure to review the notes that are provided for this section while viewing the videos—the videos will solve some of the equations whose solutions are presented in the notes.

Reading Assignment Chapter 1 1.1 Slopes and Equations of Lines, pp. 2-13 1.2 Linear Functions and Applications, pp. 17-23 Chapter 2 2.1 Solution of Linear Systems by the Echelon Method, pp. 45-52

Supplemental Reading Chapter 1 Review: Summary, pp. 38-39 Chapter 2 Review: Summary, pp. 104-105

Learning Activities (Non-Graded) See information below.

Key Terms 1. Break-even

quantity/point 2. Cost function 3. Echelon method 4. Equilibrium price/

quantity 5. Fixed cost 6. Linear equation 7. Marginal cost 8. Parallel line

MA 1140, Finite Math 2

Section 1.1 Video Tutorials and Notes:

 Click here to access video 1.1: How to Find Slopes.

 Click here to access video 1.1: Equations of Lines.

 Click here to access video 1.1: Parallel and Perpendicular Lines.

 Click here to access a PDF of the Section 1.1 Notes. Section 1.2: Linear Functions and Applications Next, we learn about linear equations and their applications. Linear equations are used in myriad real-life scenarios, including figuring out supply and demand, as well as surplus; performing a cost analysis; and determining a cost function or a break-even analysis. The textbook covers this topic in Section 1.2 (pp. 17-23). After reading the textbook and viewing the examples it provides, view further examples provided in video tutorials demonstrating additional solutions. Be sure to have the notes open so you can follow along with them as the videos progress. Section 1.2 Video Tutorials and Notes:

 Click here to access video 1.2: Function Notation

 Click here to access video 1.2: Supply and Demand

 Click here to access video 1.2: Cost Functions, Breakeven Values, and Profit

 Click here to access a PDF of the Section 1.2 Notes. Section 2.1: Solution of Linear Systems by the Echelon Method The final topic of Unit I addresses using the echelon method to solve linear systems. As the textbook states on page 47, “The goal of the echelon method is to use the transformations to rewrite the equations of the system until the system has a triangular form” (Lial, Greenwell, & Ritchey, 2012). Why is this important? Read Section 2.1 to find out. How to solve linear systems by using the echelon method is covered in the textbook in Section 2.1 (pp. 45-52). Read the textbook, study the examples, and then access the notes and the videos that provide explanatory examples. Be sure to have the notes open so you can follow along with them as the videos progress. Section 2.1 Video Tutorials and Notes:

 Click here to access video 2.1: Intro to Systems of Equations

 Click here to access video 2.1: Row Echelon Method

 Click here to access video 2.1: Multiple-Step Row Echelon Method

 Click here to access a PDF of the Section 2.1 Notes. After you complete the above, the next step is to complete the Homework assignment. You must achieve a minimum 70% score on the Homework in order to be able to access The Unit Assessment for Unit I. The Unit Assessment will assess your mastery of the unit content. If you have any questions or difficulties concerning any of the concepts in this unit, contact your instructor for additional information and guidance. Both the Homework and the Unit Assessment are available in MyMathLab.


Lial, M. L., Greenwell, R. N., & Ritchey, N. P. (2012). Finite mathematics (10th ed.). Boston, MA: Pearson.

9. Parameter 10. Perpendicular line 11. Profit 12. Revenue 13. Slope 14. Slope-intercept form 15. Surplus

MA 1140, Finite Math 3

Learning Activities (Non-Graded) Practice What You Have Learned

After reading Sections 1.1, 1.2, and 2.1, improve your mastery of the content by working the Exercises that pertain to each section:

 Section 1.1 Exercises are on pages 13-14.

 Section 1.2 Exercises are on page 23.

 Section 2.1 Exercises are on page 52. Apply What You Have Learned After you have mastered the mechanics of the mathematics in Unit I, apply what you have learned to solve a variety of real-life situations in each of the assigned sections:

 Section 1.1 Applications are on pages 14-16.

 Section 1.2 Applications are on pages 23-25.

 Section 2.1 Applications are on page 53-54. Review What You Have Learned Before attempting the Homework and the Unit Assessment, read the chapter summaries, and review the concepts taught in Unit I by completing the following Review Exercises:

 Chapter 1 Review Exercises: pp. 39-40; numbers 1-57

 Chapter 2 Review Exercises: p. 106; numbers 3, 4, 19-22, and 66 MyMathLab Study Plan for Unit I The Study Plan, located in MyMathLab, will provide you with additional practice for concepts and information, based on the Practice Exercises, Homework, and Chapter Review you completed in MyMathLab. It is generated specifically for each student based on your results, detailed to provide practice where it is needed for mastery of the unit concepts. Once you have accessed the MA 1140 course in MyMathLab, click on “Study Plan” in the menu on the left side of the screen, and find the information pertaining to Unit I. Other Resources and Activities If you need additional guidance or information, access the Multimedia Library in MyMathLab to see Animations that show how to solve selected types of problems, Video Lectures, PowerPoints, and Interactive Figures for information about a variety of topics from this unit. The Multimedia Textbook is an electronic version of your textbook. To access the Multimedia Library, click on “Multimedia Library” in the toolbar on the left side of the screen. When the dialog box comes up, select the chapter, section, and media types from the dropdown menus, and then click “Find Now.” This will bring up a listing of media assets that you can click on to view. NOTICE: These are all non-graded Learning Activities, so you do not have to submit them. If you experience difficulty in mastering any of the concepts, contact your instructor for additional information and guidance.

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