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Given a diagram where the x axis is the horizontal one and the y axis is the vertical one. Which of these alternatives are the right and or best way of writing it:

  1. plotting x against y
  2. plotting y against x
  3. plotting x versus y
  4. plotting y versus x

My (Swedish) brain wants alternative 1 or 3 but there are sources pointing in other directions. Could this be a case where different languages do different ordering? I would expect these mathematical 'things' to be standardized among languages but now I am not so sure...

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6 Answers

up vote 4 down vote accepted

So, for simpler rule of thumb, I use: Wall against ground
So, whatever is your independent quantity, is usually plotted on the horizontal axis, as if it needs no support, like time. And the other quantity that needs support is plotted on (parallel) to the vertical axis. But of course, thats just to simplify things. In cases like Voltage and Current, we can interchangeably plot them, as V=IR, since both can be related to depend on each other, depending on what relationship you are trying to deduce. But to finally answer your question, the more common way to do so would be:

Vertical axis against/versus Horizontal axis.

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Usually, the standard graph is a plot of the dependent variable against the independent variable

(from a physics society forum at http://www.physics.nus.edu.sg/~physoc/forum/archiver/?tid-48.html ).

The independent variable is normally plotted along the horizontal axis.

However, though in physical relations there may often be an obvious candidate for the independent variable, in pure mathematical equations, it is a matter of choice - often convenience - which one is chosen as subject of the formula. Also, there may be a reason to break with convention and swap the x-axis and y-axis over.

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So, using the naming conventions from my example, plotting y against x? Vertical against horizontal? –  jonalv Mar 19 '13 at 8:35
    
"Vertical against horizontal", and, if you choose the almost (but not quite) universal convention of having x-values along the horizontal axis, and the variables are x and y, 'y against x'. There is the complication that the horizontal axis is usually called the 'x-axis'; this doesn't matter when you're plotting v against t (or t against v), say, but if you wish to plot x against y, you've got problems with the names of the axes. –  Edwin Ashworth Mar 19 '13 at 9:12
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x and y are dummy variables, but often used by standard convention as dimensional representations of the Cartesian plane. An independent variable is represented by the abscissa (e.g. 'x'), and the depedendent variable as the ordinate (e.g. 'y').

As the value of the function y, where y = f(x) represents an instance where the value of y is dependent upon the value of x, it would be correct to say that y is plotted against x rather than the other way around.

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'X' is independent; whereas 'Y' is dependant on 'x'. Why prominence is given to dependant term? As the value of 'Y' depends on 'X', I feel, we have to say," plot of 'X' vs 'Y' "

It is just a common mans' perception but there may be sound mathematical logic behind the scene. To just know that fact, I was surfing; though I came across this discussion, yet I am not fully convinced, why 'Y' has to be mentioned first, when it is a function of 'X'. I am not an expert in this field, but a novice.

T.S.Rao

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This question should be asked in the Mathematics department.

Usually, plotting against x is a plot of function f(x) against a horizontal value of x:

f(x)

Therefore, plotting y against x

y = f(x)

which is a mapping of y values against a range of x values related thro the function f(x).

OTOH, when mathematically necessary, we would also plot x against y,

x = f(y)

The convention is that x would occupy the horizontal axis, while y occupies the vertical axis, regardless if x is plotted against y, or y against x. Visually, which often would appear mutually indiscriminatable for 1-1 mapping plots. For higher order graphs, it would be rather obvious what is being plotted against which. For example, quadratic functions and open-curve conics,

v <-> u

such that there are more than one value of u for every v, but only one value v for every u, it is quite obvious we should be conveniently plotting v against u, regardless of the orientation of their respective axes.

In the case of closed-conics: circles and ellipses, there is no difference in plotting vert against horz or horz against vert because there are always two values of v for each value of u, and similarly two values of u for each value of v.

However, if neither dimensions are specified in terms of x or y, for example, ROI against Investment, we would usually make ROI the vertical axis and Investment the horizontal axis. But that is not an exclusive practice.

This answer should be answered by a Math professor for 1st year Math students. This is not a question concerning the English language, because you would face the same dilemma whether you approach in Russian, Hindi, Swedish or Tagalog.

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Your so-called "convention" that a variable x "would occupy the horizontal axis" is utter nonsense. The independent variable plotted on the horizontal axis may be assigned the label x if there is not a more appropriate one (such as t for time or c for concentration). There is no converse. If you do not understand the use of the (English) terms dependent and independent variable as explained in the other responses, it might be best if you stay away from questions that could be answered by a teacher of high school mathematics. –  Fortiter Mar 19 '13 at 1:46
    
+Fortiter, thx. Venting is a healthy exercise. –  Blessed Geek Mar 19 '13 at 2:24
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When describing a relationship that is represented on a cartesian graph, the correct form is

dependent variable against the independent (or manipulated) variable.

This reflect the fact that the value of the dependent variable is responding to, or following, changes in the independent variable. While it is common in classroom conversation to use the Latin versus rather than the English against, this should be avoided in formal writing because for many readers it carries a connotation of opposition that is inappropriate.

Your question embodies two separate mathematical conventions. The independent variable should always be plotted on the horizontal axis and it MAY be represented by the label x if there is not another more evocative label (such as t for time or c for concentration).

An example drawn from Chemistry might be

Figure 2.3 plots the rate of reaction r (in mL of hydrogen per minute) against the concentration of acid c (in moles per litre).

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Your perspective is too restricted to your own field of expertise. –  Blessed Geek Mar 19 '13 at 2:15
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