Talk:Linear equation

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[edit] Side of a line?

Given a point and a line in a plane, how do you determine what side of the line the point is on?

Given an arbitrary plane and a point and line in that plane, how do you even characterize which side of the line is which? It's (relatively) easy if the plane is the usual x-y coordinate system: you can see whether the point is to the left or right, or above or below the line (for example, solve the linear equation for y and plug in the x coordinate of the point, then see if the y coordinate of the point is greater or less than the y given by the equation -- or reverse everything and compare the x values). In higher dimensions (e.g., an arbitrary 2-D plane in 3-D space), it seems that it would be a little harder to even define the problem you're trying to solve. - dcljr (talk) 23:53, 7 November 2005 (UTC)

[edit] Math formatting

For consistency I have changed equations not in-line to Math formatting. Hope there are no problems with this. michaelCurtis ^talk+_{contributions} 09:54, 31 May 2006 (UTC)

[edit] Introduction, variables, and formatting

I have a few gripes to express about the current (and aggressively defended) version of the page:

1. The introduction provides an example of a two-variable equation in slope-intercept form. Why? It should provide an example of a generic, multivariable equation, as linear equations are in no way limited to two variables. If it doesn't fall in the introduction (and I think it should), it should at least be covered SOMEWHERE in the article.
2. The article uses atypical variables. For one thing, m, h, and k, as used in this article, are never capitalized (though this article seems insistent upon capitalizing them). For another, h and k are used with conics (representing centers and vertices), not linear equations (which have no centers or vertices). It is common to use (x₁,y₁) to represent any point on the line (as h and k apply undue significance to that point).
3. Variables should always be italicized. Period.
4. There is no reason to indent the paragraphs of the two-variable linear equation forms.
5. Wording and voice should remain relatively consistent.

I tried to correct most of these, but my edit was quickly reverted. I would like to see some discussion as to why.—Kbolino 16:02, 2 February 2007 (UTC)

Hi Kbolino. Sorry for my perhaps ore hasty revert of your changes. I have some issues with them, but I don't have the time at present to discuss them. So if you feel strongly about them please revert back. Perhaps I will have the time to discuss this later. Regards Paul August ☎ 16:48, 2 February 2007 (UTC)

Ok, I've had some time to consider your proposed changes:

1. I think the introduction of n-dimensional linear equations is better postponed until further along in the article. I have added a new section for this.
2. I think the use of capital letters to designate constants is ok, it is certainly not uncommon. It does help to distinguish the variables from the constants, but I've restored your changes.
3. Yes, I think they all are now.
4. Yes.

I also noticed that when you found the article, it was in a vandalized state, with the slope-intercept form labeled "Point-slope form", and the real slope-intercept form having been deleted, which to your credit you of course fixed.

I hope this addresses all your concerns. If not I am happy to discuss all this further. Again I apologize for my hasty revert.

Regards, Paul August ☎ 21:16, 2 February 2007 (UTC)

I appreciate your patience. I can get a bit testy sometimes (that's an understatement, by the way). I understand your reasoning behind capitalizing the constants—in a way, it does make things clearer. I've just never seen them that way and it's foreign to me (which makes them, for me, ironically less clear).

What I meant by the statement about indentation was not a complaint about the headings (I think it was a good idea to have them), but about why they were indented beneath those headings.

As for H and K, I don't fully understand where they came from—I've only ever seen them used with conics. The points I usually see as (x₁, y₁), (x₂, y₂)—but this isn't necessarily clear for everybody, and it could lead to confusion with the generic multivariable syntax.

The thing that really got me about capitalization was M (for slope), which I have never in my life seen capitalized (limited range of experience, mind you). I'm not too pragmatic about capitalization—in math, M and m are two different letters to me. It's like throwing g out there for slope.

And the note about voice was in reference to the use of where and here to begin descriptions of formulas. Either one works for me, but the article should try to be consistent; though I'd rather one or the other was used than neither.

I'm going to make an edit to reflect some more of my changes, try to compromise, and see where that turns out. If you don't like it, then please don't just revert—that's what gets me riled up—if one or two things bother you, then just change those things back. I often change things as they scroll by, which means they can easily go unnoticed on reading an edit summary or viewing a diff.—Kbolino 22:55, 2 February 2007 (UTC)