How to Find the Points of Intersection on a TI84 Plus Graph
The Pt of IntersectionTrace option on your TI84 Plus is used to find the points of intersection appearing on the graph screen. When the calculator finds such a point, you can store the x– and ycoordinates of that point in the calculator. This is quite handy when solving linear programming problems. To find and store the points of intersection in an inequality graph, follow these steps:

Press [ALPHA][ZOOM] or [ALPHA][TRACE] to select the Pt of IntersectionTrace option.
Because the Pt of IntersectionTrace option at the bottom of the graph screen is above the F3 and F4 function keys on the calculator, this option can be selected by pressing either [ALPHA][ZOOM] to select F3 or [ALPHA][TRACE] to select F4.
After selecting this option, the cursor moves to one point of intersection and the coordinates of that point are displayed at the bottom of the screen, as illustrated in the first screen. In the upperleft corner of the screen, you see the names of the intersecting inequalities.

To store the coordinates of the point of intersection, press
If you don’t need to store these coordinates, you can skip this step. If you do press
you get a message saying, “Point appended to (∟INEQX, ∟INEQY),” as shown in the first screen. This tells you that the xcoordinate is stored in the list named INEQX and the ycoordinate is stored in list INEQY. Press [ENTER] to get rid of the message and return to the graph.
If the point is already stored in the calculator, you get the “Duplicate Point” message as shown in the second screen. Press [ENTER] to get rid of the message. The Inequality Graphing app will not store the point a second time.

Use the arrow keys to move to the next point of intersection and, if you desire, store its coordinates by pressing
Pressing the left or rightarrow key moves the cursor to the next point of intersection on the graph of the left inequality in the upperleft corner of the screen. This is illustrated in the first and second screens. In the first screen in this figure, the left inequality in the upperleft corner of the screen is Y1.
After you press the uparrow key the cursor jumps to the other point of intersection on this line, as illustrated in the second screen. Because this line has only two points of intersection, if you were to press the uparrow key again, the cursor would go back to the point of intersection in the first picture in this figure.
Pressing the up or downarrow key changes the left inequality in the upperleft corner of the screen. This may or may not move the cursor. If the cursor doesn’t move, press the left or rightarrow key to move the cursor to the next point of intersection.
For example, to get from the second to the third screen, press the leftarrow key to change the left inequality to X1. But this gave you the intersection same point of intersection. So press the leftarrow key to get the other point of intersection on line X1, as illustrated in the third screen.

Press [CLEAR] when you are finished using Pt of IntersectionTrace.