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How to Find the Points of Intersection on a TI-84 Plus Graph

The Pt of Intersection-Trace option on your TI-84 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 y-coordinates 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:

  1. Press [ALPHA][ZOOM] or [ALPHA][TRACE] to select the Pt of Intersection-Trace option.

    Because the Pt of Intersection-Trace 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 upper-left corner of the screen, you see the names of the intersecting inequalities.

    image0.jpg
  2. To store the coordinates of the point of intersection, press

    image1.jpg

    If you don’t need to store these coordinates, you can skip this step. If you do press

    image2.jpg

    you get a message saying, “Point appended to (∟INEQX, ∟INEQY),” as shown in the first screen. This tells you that the x-coordinate is stored in the list named INEQX and the y-coordinate 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.

    image3.jpg
  3. Use the arrow keys to move to the next point of intersection and, if you desire, store its coordinates by pressing

    image4.jpg

    Pressing the left- or right-arrow key moves the cursor to the next point of intersection on the graph of the left inequality in the upper-left 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 upper-left corner of the screen is Y1.

    After you press the up-arrow 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 up-arrow key again, the cursor would go back to the point of intersection in the first picture in this figure.

    Pressing the up- or down-arrow key changes the left inequality in the upper-left corner of the screen. This may or may not move the cursor. If the cursor doesn’t move, press the left- or right-arrow key to move the cursor to the next point of intersection.

    For example, to get from the second to the third screen, press the left-arrow key to change the left inequality to X1. But this gave you the intersection same point of intersection. So press the left-arrow key to get the other point of intersection on line X1, as illustrated in the third screen.

  4. Press [CLEAR] when you are finished using Pt of Intersection-Trace.

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