The two-dimensional Cartesian coordinate system may be used to graph a variety of equations in the form of straight and curved lines. One way to graph an equation is to determine a number of different values for the variables and plot them on the graph. It can be helpful, however, to understand how a change in the parameters of an equation affects the resulting line.

Graphs of Straight Lines

The graph of the simple equation y = 1x, or y = x, is graphed in (a) below. The line passes through every coordinate point where x = y, such as (2, 2) or (–3, –3).

Notice what happens to the graph of the equation when the parameters of the equation are changed by using a different coefficient for x, such as y = 3x. As part (a) shows, the new line has a steeper slope. If...