Graphing Equations with a Graphing Utility

Most graphing calculators require similar techniques to graph an equation. The equations sometimes have to be manipulated so they are written in the style y=_____. The TI-84 Plus, and many other calculator makes and models, have a mode function, which allows the window (the screen for viewing the graph) to be altered so the pertinent parts of a graph can be seen.

For example, the equation [latex]y=2x - 20[/latex] has been entered in the TI-84 Plus shown in Figure 9a. In Figure 9b, the resulting graph is shown. Notice that we cannot see on the screen where the graph crosses the axes. The standard window screen on the TI-84 Plus shows [latex]-10\le x\le 10[/latex], and [latex]-10\le y\le 10[/latex]. See Figure 9c.

This is an image of three side-by-side calculator screen captures. The first screen is the plot screen with the function y sub 1 equals two times x minus twenty. The second screen shows the plotted line on the coordinate plane. The third screen shows the window edit screen with the following settings: Xmin = -10; Xmax = 10; Xscl = 1; Ymin = -10; Ymax = 10; Yscl = 1; Xres = 1.

Figure 9 a. Enter the equation. b. This is the graph in the original window. c. These are the original settings.

By changing the window to show more of the positive x-axis and more of the negative y-axis, we have a much better view of the graph and the x- and y-intercepts. See Figure 10a and Figure 10b.

This is an image of two side-by-side calculator screen captures. The first screen is the window edit screen with the following settings: Xmin = negative 5; Xmax = 15; Xscl = 1; Ymin = -30; Ymax = 10; Yscl = 1; Xres =1. The second screen shows the plot of the previous graph, but is more centered on the line.

Figure 10 a. This screen shows the new window settings. b. We can clearly view the intercepts in the new window.

Example 3: Using a Graphing Utility to Graph an Equation

Use a graphing utility to graph the equation: [latex]y=-\frac{2}{3}x-\frac{4}{3}\\[/latex].

Solution

Enter the equation in the y= function of the calculator. Set the window settings so that both the x- and y- intercepts are showing in the window.

This image is of a line graph on an x, y coordinate plane. The x-axis has numbers that range from negative 3 to 4. The y-axis has numbers that range from negative 3 to 3. The function y = -2x/3 + 4/3 is plotted.

Figure 11