SAMPLE College Algebra

Chapter 1: Linear Functions

OVERVIEW The sections of this chapter are: 1.1 Graphs 1.2 Visual Linear Functions 1.3 Solving for an Unknown 1.4 Algebra of Linear Functions

1.5 Systems of Equations 1.6 Interpret and Apply

In the book Making Learning Whole, the author David Perkins wrote "Math is usually taught with an overemphasis on dry, technical details, without giving students a concept of the whole game." David Perkins is a senior professor of education at the Harvard Graduate School of Education. OBJECTIVES By the end of the chapter, a student will be able to: • Understand the difference between linear and nonlinear equations

• Understand the real meaning of a function • Work with linear expressions and equations • Interpret and apply linear functions 1.1 Graphs

The coordinate plane is also called the Cartesian Coordinate plane. The coordinate plane makes it possible to describe space in 2 dimensions. Space in 2 dimensions is infinite, or endless. In order to measure and describe, points of reference are necessary. A coordinate plane provides points of reference and the main point of reference is the origin, that is shown, just below, with a red dot. To review, the coordinate plane consists of a horizontal axis that is labeled x , and it is called the x-axis. Notice that the x-axis has an arrow at each end. This is because space continues in that direction. Still practical use of the coordinate plane will display a sample or small piece of space. There is also a vertical axis labeled y , and it is called the y-axis. Notice that the y-axis has an arrow on each end. This is because space in 2 dimensions continues without end. Below, just to the right, one can see a coordinate plane . It basically consists of a horizontal x-axis, and a vertical y-axis. Below, a few characteristics of this particular graph are listed.