In the last chapter, we graphed data. Now, we move to graphing equations with two variables. For simplicity, the discussion in this chapter is confined to linear equations, i.e. equations of degree 1. Some of the general concepts carry over to more general equations, to be discussed later.
The first section explains how to represent variables as ordered pairs. This is a convenient way of writing corresponding variable values. In this section, we will also learn how to graph ordered pair values (x, y) on an xy-graph. Graphing (x, y) values on a graph is similar to graphing x values on a number line, except that we are working in two dimensions instead of one.
The second section provides an introduction to graphing equations. It explains how to make a data table of (x, y) values and how to make a graph from a data table.
There are several methods of graphing equations. The next section introduces another method of graphing linear equations using the x-intercept and y-intercept. It is similar to creating a data table, but often quicker.
The fourth section explains the concept of slope. Slope is a characteristic of a linear equation that will allow us to graph that linear equation, recognize its graph, and understand how it relates to other linear equations.
The final section introduces a third method of graphing linear equations, which uses slope. It explains how to graph a linear equation given its slope and a single point, and it explains how to determine the slope of a line, given its equation.
Graphing is an enormous topic in algebra I and algebra II. No matter what type of equations you study in future algebra, you will probably need to know how to graph them. Thus, it is important to understand the material in this introductory chapter. Each method of graphing learned here will become useful in later topics in algebra, pre- calculus, and even calculus.
Graphing also has practical applications. Chemists and physicists use graphs to discover relationships between quantities. Graphs can be used to predict future values of important figures like population and the national debt. Graphs are used in almost every discipline, so it is important to develop an understanding of how to use them.