Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 356

When the y axis is labelled x

On a basic co-ordinate system is the horizontal axis always x, and the vertical axis always y?
And if they’re not labelled should we always think of them like that? Should they always be labelled? Is it considered slack when they’re not?
What about a position/time graph, where the y axis is labelled x for position? Is this often confusing for the novice?

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Bob

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Registered: 2010-06-20

Posts: 10,654

Re: When the y axis is labelled x

The correct terms for the across and up axes are abscissa and ordinate. Descartes thought up the coordinate system and used x and y, so those have kind of stuck.  The page where I found the definitions of  abscissa and ordinate even used x and y to explain which is which

So it is good practice to always label each axis and it's perfectly ok to use your own symbols where the context suggests it (such as t across for time).

It is also usual to make x the independent variable (ie. the one whose values we can choose) and y the dependent variable (ie. the one whose values depend on a formula involving x).

But usual, not compulsory.

In 3D coordinates x is usually shown going right, y going back into the page, and z going up.

Is it confusing? Yes, probably, but using x for time would be worse I think.  A graph is just a way to make a picture out of a mathematical model and usually helps. Choosing the right variables will help if the grapher says what and why.

Saying at the start what symbols you're going to use is essential.  In logic there are several ways to indicate logic operators such as AND, OR, IMPLIES etc. And it is common to use a dot to replace a multiplication symbol to avoid confusion with a variable x.  In an Argand diagram the up axis labels have an 'i' to indicate an 'imaginary' number, but some folk use 'j'.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Phrzby Phil

Member

From: Richmond, VA

Registered: 2022-03-29

Posts: 59

Re: When the y axis is labelled x

An interesting exercise in an algebra class is to treat y (vertical axis) as the independent variable, and define and graph x = f(y).
E.g., parabolas are "sideways," functions must pass the horizontal line test, etc.

If defining functions depending on time, I would definitely use t as the independent (horizontal) variable.

Use whatever makes sense to help keep track of what's going on.

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paulb203

Member

Registered: 2023-02-24

Posts: 356

Re: When the y axis is labelled x

Thanks, Phil.

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Prioritise. Persevere. No pain, no gain.

paulb203

Member

Registered: 2023-02-24

Posts: 356

Re: When the y axis is labelled x

Thanks, Bob.

Although when I Googled abscissa and ordinate the first few results said those were names for the x and y co-ordinates, not the axes themselves.

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,654

Re: When the y axis is labelled x

That's a fair description.  I'll stick to across and up in the future.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 356

Re: When the y axis is labelled x

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Prioritise. Persevere. No pain, no gain.