Mathematics 209: Finite Mathematics

Study Guide

Unit 1: Linear Equations and Graphs

Lines are the simplest geometric elements, and the most useful in mathematics. In this unit, we sketch linear equations and describe regions defined by linear inequalities.

Objectives

When you have completed this unit, you should be able to

1. solve linear equations.
2. solve linear inequalities.
3. plot points on the Cartesian coordinate plane.
4. sketch linear equations.
5. identify the slope of a line.
6. interpret the slope of a line as a rate of change.
7. apply linear regression to find a function that provides a mathematical model for a set of data points.

Linear Equations and Inequalities

Indications

1. Read Section 1-1, Linear Equations and Inequalities, on pages 3–11 of the textbook.
2. Do odd-numbered exercises 1–39 on page 11 of the textbook. If you have difficulty, consult your tutor to discuss the problem.
3. Solve odd-numbered problems 53–67 on pages 12–13 of the textbook. If you have difficulty, consult your tutor to discuss the problem.
4. Answer the questions listed below, and then compare your answers with those given in the Answers to Study Guide Questions.

Questions

1. What is a linear equation?
2. What is a linear inequality?
3. What is a break-even analysis?
4. Is it true that all numbers in the interval $[4,\infty ]$ satisfy the linear inequality $3x-5>7$?
5. What is the slope of a line that passes through two points, $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$?

Graphs and Lines

Indications

1. Read Section 1-2, Graphs and Lines, on pages 13–25 of the textbook.
2. Do odd-numbered exercises 1–33 and 41–53 on pages 25–26 of the textbook. If you have difficulty, consult your tutor to discuss the problem.
3. Solve odd-numbered problems 57–67 and 75 on pages 27 and 28 of the textbook. If you have difficulty, consult your tutor to discuss the problem.
4. Answer the questions listed below, and then compare your answers with those given in the Answers to Study Guide Questions.

Questions

6. What is a linear equation in two variables?
7. What is an equation of a horizontal line?
8. What is an equation of a vertical line?
9. What is an equilibrium point?
10. When is the slope of a line zero?

Linear Regression

Indications

1. Read Section 1-3, Linear Regression, on pages 29–37 of the textbook.
2. Solve problems 1–21 on pages 37–40 of the textbook. If you have difficulty, consult your tutor to discuss the problem.
3. Answer the questions listed below, and then compare your answers with those given in the Answers to Study Guide Questions.

Questions

11. Why is the slope of a line with variables $x$ and $y$ defined as the rate of change of $y$ with respect to $x$?
12. What is a set of data?
13. What is regression analysis?
14. What is a linear regression?

Finishing This Unit

1. Review the objectives of this unit and make sure you are able to meet each of them.
2. Study the section of the Chapter 1 Review titled Important Terms, Symbols and Concepts, on pages 42–43 of the textbook.
3. If there is a concept, definition, example or exercise that is not yet clear to you, go back and re-read it. Consult your tutor if you need help.
4. You might want to do all or some of the exercises from the Review Exercise section on pages 43–45 of the textbook. The questions on the practice examination are taken from this exercise. If you have difficulty, contact your tutor to discuss the problem.
5. Complete the practice examination provided for this unit. Evaluate yourself, first checking your answers against those provided in the Answers section at the end of the textbook, and then comparing your solutions with those provided on pages S-26 to S-33 of the Student Solutions Manual portion of the textbook. The number of points in a question may indicate the number of steps in the solution. Give yourself full credit if your answer is correct and you give a complete solution, even if your solution differs from that shown in the Student Solutions Manual.

Practice Examination

Time: 1.5 hours
Total points: 30
Passing grade: 50%

Do the following exercises from the Chapter 1 Review Exercise on pages 43–45 of the textbook.

To obtain full credit you must justify all your answers and show your work.

1. Exercise 10  (Marks: 5 pts)
2. Exercise 18  (Marks: 4 pts)
3. Exercise 24  (Marks: 5 pts)
4. Exercise 36  (Marks: 6 pts)
5. Exercise 41  (Marks: 10 pts)