Graphs: problem displaying a 3rd straight line

But how did you get the 'whatevervariable' bit you placed (which I have now replaced with the 3rd variable y_3), below y_2 to display on the left hand-side, next to the y-axis? I double-clicked on the graph area and various places but all I can only see are the changes in the Traces section.

I think now that I had misunderstood your first posting. I thought you had set the two vertical markers at x0 and x1 and wanted a third vertical line, so I showed how to do that. Now it seems to me that you did not create the graph yourself in the first place and your problem was to add the graph of other functions to the two already here. You can do that by typing a commy after the function name, lets say after y1(x), and you get a placeholder to fill in. The same goes for the x-axis (here you see the commatas). If the plot you posted is what you are after it would not be necessary to have the three "x" on the abscissa. If there is only one variable there Mathcad would take it for all the functions on the ordinate. It was only necessary as I added a vertical line and needed a constant value on the abscissa, so I had to tell MC which value would belong to which graph. But there is nothing bad to provide an x for every function plotted.

The thing you tried to change is called legend. To change it double click the plot or choose frome the menu "Format/Graph/xy-plot" choose tab "Traces" and in the first column (Legend label) you can type in what you see if you choose to show a legend (which is by default hidden).

Is it because you have MCad Prime hence can make there relevant changes?

God, no! I don't use Prime on a regular basis. Prime lacks a lot of the features Mathcad 14 or 15 already have and is terrible slow on my machine. Here and there, though, it has some nice new features (which don't compensate for the missing ones) and one of those is the ability to add more vertical markers in a 2D plot. But then, in Prime you don't have a Legend at all but would be forced to place text boxes by hand over the graph region!. Prime also is not able to read and write files in "old" Mathcad format. You would need the current version of MC15 installed along with Prime2 to be able to convert older files to the new Prime format and there is no way back. You may have already gueesed it, I don't like Prime 😉

And how can I change the y-axis to go past the intersect of y=3-x between a range, for instance, y_0 = -1 and y_1 = 5 ? It seems that I can only set the x-axis , which at the moment are x_0 = -2 and x_1 = 6.

You can change the range of the y-axis the same way as that of the x-axis. At the x-axis you see at the ends to the left and right of the "x,x,x" the limits, which are set to the variables x.0 and x.1. The same way you can see at the ends of the y-axis, above and below the list of y..(x) the values -1 and 3. Feel free to change them. If you delete one of these values and don't type in a new one, Mathcad will automatically choose a suitable value for you.

Last but not least, if I were to update my currention version of MathCad (Mathcad 14.0 ) to the student edition of MathCad Prime 2.0 , would there be more options?

In the meantime you know my feelings about Prime. Even from MC14 to Prime2 I would consider it a downgrade. If you would have the opportunity to update tp Mathcad 15 I would call this a good idea. But you can judge yourself - download the eval edition of Prime2 from the PTC homepage and install it. You don't have to deinstall your MC14 to do so - they exist parallel. After the 30day trial period Prime would transform to a crippled version which PTC calls Prime Express. You can still work with it but a bunch of features will be deactivated (solve blocks, symbolic operations,..?) Also, if you do not want to loose your MC14 installation you cannot install the eval of MC15 and so you would not be able to convert Worksheets from the older format to Prime format. But in this case I am sure that if you post it here someone will be willing to help and do the conversion for you.