I assume your data should be plotted with concentration or pressure (depending if you are doing an aqueous or gas phase adsorption experiment) on the x-axis and uptake on the y-axis. For example see my paper (Article Cation Dependant Carbonate Speciation and the Effect of Water
), where the adsorption isotherm is plotted with pressure on the x-axis and uptake on the y-axis. Assuming you are doing an experiment similar to the equation your provide, this would be Ce on the x-axis and Qe on the y-axis.
I think your question is possibly about fitting the Langmuir equation to your data? If so, you will need to plot your data as above, use a program like OriginPro or Excel Solver to fit the equation. Set Ce as x and Qe as y. Set Qmax, Kl and S as parameters. Allowing the program to fit the data will give you values for these constants. See a similar example here (https://www.youtube.com/watch?v=WLj6bblDFS8).
I hope this helps, let me know if anything is unclear.
In any graph the independent parameter should be on the horizontal axis. The dependent parameter on the vertical axis. The X or Y axis you mentioned is just a conventional symbol used in mathematics. If you put parameter, k and it causes L to change, then such a plot would be made by plotting L on the vertical axis and k on the horizontal.
I think you are having trouble with rearranging the equation. Just inverse the both sides so you will get 1/Qe =( a+b+c)/def. Now devide each a, b and c by denominator so you have a nice y = mx + C type equation.