The graph of an equation is the set of points corresponding to all ordered pairs that satisfy the equation. It gives a “picture” of the equation. Most equations in two variables are satisfied by an infinite number of ordered pairs, so their graphs include an infinite number of points.
To graph an equation, we plot a number of ordered pairs that satisfy the equation until we have enough points to suggest the shape of the graph. For example, to graph 2x + 3y = 6, we plot all the ordered pairs found in Objective 2 and Example 1 on the previous page. These points, shown in a table of values and plotted in Figure 4(a), appear to lie on a straight line. If all the ordered pairs that satisfy the equation 2x + 3y = 6 were graphed, they would form the straight line shown in Figure 4(b).
The equation 2x + 3y = 6 is called a first-degree equation because it has no term with a variable to a power greater than one.
The graph of any first-degree equation in two variables is a straight line.