How to find the intersection of two lines graphically using the TI-83

Let’s graph the line y = 2x − 1 Begin by pressing the “y =” key, just below the left corner of the screen. Each line y1, y2, y3, represents a different function to be graphed.

Enter “2x − 1” on the top “y =” line. To enter the “x” in the function, use the key indicated by the arrow. It reads “x, T, O, n”

To graph this line, so that everyone’s screen looks alike, we are going to use the “zoom” button, in the middle of the top row. For this line we will use “zoom, decimal.” To get this, we press “zoom”, then “4.” Later, we will be using this zoom key to explore the intersections of graphs.

Here is the result. If anyone’s line looks different from the one pictured, we need to change some settings on the calculator.

Next, we will add another line to the graph. We are going to add the line y = −x + 2. First, hit the “y =” button again. Then, scroll down to the second “y =” line. Since this function starts with a “minus” sign, we need to enter it a little differently. The problem is that this calculator has both a “minus” key and a “negative” key. At the beginning of a function, we need to use the “negative” key. Enter “−x+2,” using the “negative” key. Then press the “graph” key.

After hitting “graph,” this screen should result. If anyone does not have this screen, we will trouble-shoot that problem. Now that both lines are on the screen, if we press any of the four arrow keys, a cursor will appear. The cursor may be moved to the intersection of the two lines.

At the bottom of the screen, the x and y values appear.

After moving the cursor to the intersection of the two lines, zoom in, by pressing “zoom,” then “2”, then “enter.” The result shows clearly that the lines intersect at the point (1, 1). Now it is time to verify that solution using algebra…