How to Finding the Points of Intersection
When a graph is displayed in Inequality Graphing on the TI84 Plus calculator, PolTrace is one of three options that appear at the bottom of the screen. The PolTrace option 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 PolTrace option.
Because the PolTrace 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 F1 or [ALPHA][TRACE] to select F2.
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. In the upperleft corner of the screen, you see the names of the intersecting inequalities.

Press
to store the coordinates of the point of intersection.
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).” 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. Press [ENTER] to get rid of the message. The Inequality Graphing application will not store the point a second time.

Use the arrow keys to move to the next point of intersection and, if you desire, press
to store its coordinates.
Pressing
or
moves the cursor to the next point of intersection on the graph of the left inequality in the upperleft corner of the screen. In the first image, the left inequality in the upperleft corner of the screen is Y1. After you press
the cursor jumps to the other point of intersection on this line, as illustrated in the second image. Because this line has only two points of intersection, if you were to press
again, the cursor would go back to the point of intersection in the first picture in this figure.
Pressing
or
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
or
to move the cursor to the next point of intersection.

Press [CLEAR] when you are finished using PolTrace.