How to Graph X in Terms of Y on a TI-84 Calculator

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The TI-84 calculator offers a number of built-in functions to solve and graph equations. Unfortunately, its core graphing options are limited to functions and equations that feature ​Y​ in terms of ​X​. It's less common that you'll need to graph ​X​ in terms of ​Y​, but if you do then the existing options won't quite cut it. Fortunately, the TI-84 allows you to import external apps and use them in much the same way as you would use the apps that ship with the calculator. The community-supported TI Calc repository contains a number of these external apps, including an app called XGraph by Joel Smith that lets you graph ​X​ in terms of ​Y​.

What Does X in Terms of Y Mean?

For most equations, you graph ​Y​ in terms of ​X​. What this means is that your equation is based on the value of ​Y​, and it's interpreted through the value of ​X​; an example of this would be ​y​ = ​x​ + 1. The value of ​Y​ depends on what the value of ​X​ is, so for each ​X​ the corresponding ​Y​ value is equal to that ​X​ value plus 1. Graphing ​X​ in terms of ​Y​ turns this around. Instead of ​y​ = ​x​ + 1, you would create a graph out of ​x​ = ​y​ + 1. In this case, your ​X​ value is dependent on the value of ​Y​ and to calculate each ​X​ you take its corresponding ​Y​ value and add 1. Unfortunately, this isn't easy to graph on a TI-84 calculator unless you calculate and plot individual points by hand since the TI-84 doesn't have an "X=" option in its graphing functions.

Installing XGraph

One thing that the TI-84 does have is a means of expanding its functions via coded apps and programs. The XGraph app takes care of this, allowing you to enter your equations in the form of ​X​ in terms of ​Y​ and graph them. The file download comes in a .zip file that contains XGRAPH.8XP and a readme file; extract the XGRAPH.8XP file to an easy-to-access location. Connect your TI-84 calculator to your computer using the USB link cable that came with the calculator, and then launch Texas Instruments' TI Connect software (which is available as a free download from the Texas Instruments website if you do not already have it installed). Select XGRAPH.8XP and confirm that you want to send it to your calculator, and wait while TI Connect sends and installs the app. Once it's complete, you can close TI Connect and disconnect your calculator.

Using the App

Press the PRGM button on your TI-84 calculator and locate the "XGRAPH" entry in your program list. Press the ENTER key, causing "prgmXGRAPH" to appear on your screen; press ENTER again to launch the app. When prompted, enter your equation but use the letter ​X​ instead of ​Y​. If you were hoping to graph an equation such as ​x​ = 2​y​ + 1, your XGraph input would be "X=? 2X + 1" instead. Press the ENTER key and wait while the program draws the graph; despite entering ​X​ in your input, the graph will be drawn as ​X​ in terms of ​Y​ (which for the example above would be the graph of ​x​ = 2​y​ + 1.) Once you've finished, press the "ON" button to break the program and select "1:Quit" to exit.

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