Talk:Linear equation

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Contents

[edit] FINDING THE SLOPE

THIS SHOULD BE IN THIS PASSAGE PLEASE ADD IT MY SON IS CONFUSED —Preceding unsigned comment added by 216.231.185.94 (talk) 00:30, 14 February 2008 (UTC)

Please do not shout. It is on the page Slope, I believe. Lunakeet 11:59, 12 May 2008 (UTC)

[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)
I agree with Kbolino on the matter of presenting the general form of the equation early in the article, with the hyper plane connection. Isn't this what a linear equation defines and is therefore in its essence? In my opinion, the long section on "Forms for 2D linear equations" should not have precedence over the general definition. Regards Knut Vidar Siem 12:02, 24 May 2007 (UTC)

[edit] Normal Form

Is it just me, or does the 'value' to divide by seem more complicated than it really is?

\frac {-C\sqrt{A^2 + B^2}}{|C|(A^2 + B^2)} = \frac {-C}{|C|\sqrt{A^2 + B^2}}.

Which really simplifies down to this:

  • C < 0 or C = 0
    • \frac {1}{\sqrt{A^2 + B^2}}
  • C > 0
    • \frac {-1}{\sqrt{A^2 + B^2}}

Actually, now I know the text is technically wrong. It stated to divide by these values when you should actually multiply. Though you could say divide by \sqrt{A^2 + B^2}. Also the previous version didn't handle the case where C = 0 since it is in the denominator. I'll fix this article up for now. --Bobcat64 02:07, 7 May 2007 (UTC)

I haven't checked you're point, but here's one thing to keep in mind: it is conventional to "rationalize the denominator"; that is, if you have a radical, put it in the numerator. That's probably why it was the way it was. Dicklyon 02:55, 7 May 2007 (UTC)

[edit] What has differences from linear function

i think (many parts of) this article says about "first-degree polynomial function", and linear function does same one. and is some formulation of this article to be written in the words of linear function (which does not mean a concept of linear maps), isn't it? linear equation can be connected to hyperplane(which contains line, plane, ..., and other codimension-one affine subspaces of Euclidean spaces) or system of linear equations. i suggest "Need clean up" this article and some other related articles. sorry for my poor english, thank you. --218.251.73.163 06:26, 15 May 2007 (UTC) And as well as the fact about finding the slope of a linear should be suggested in this passage.

With regards to the general linear equation at the end of the article, isn't it wrong saying "such an equation will represent a line in n-dimensional Euclidean space"? To my understanding, such an equation represents a hyperplane, not a line; the hyperplane article supports this. Knut Vidar Siem 17:54, 23 May 2007 (UTC)

[edit] Does trigonometry apply to linear equations?

like for example the radius of a circle is equal to

x2+ y2 = radius2

Detailed

radius2 = ( x2 - x1 )2 + ( y2 - y1 )2

This equation represents the length of the radius and it uses the [Pythagorean Theorem]

Just curious --• Storkian • 22:28, 4 October 2007 (UTC)

I don't understand the question; but those equations are not linear, so the answer is probably no. Dicklyon 23:43, 4 October 2007 (UTC)

My bad that was a length equation and it disregarded slope or intercepts. --Storkian aka iSoroush Talk 23:40, 3 December 2007 (UTC)

[edit] Disambiguation?

y=mx+c is taught in the UK why is y=mx+b used here? People who do a search in the UK for example might not be able to find this article. y=mx+b leads here why not y=mx+c?

I did a search for this and found no results except for this article and a few others. Finally finding the linear equation article I realised that this is what I was looking for.

Please add y=mx+c, so that when you type in the equation it leads here.

LOTRrules 20:40, 17 October 2007 (UTC)

b and c are just variables that represent the C in the standard equation Ax+By+C=0. maybe b and c should be generalized as C. --• Storkian • 17:13, 2 November 2007 (UTC)
Done. y=mx+c now redirects here. —Celtic Minstrel (talk • contribs) 04:22, 12 December 2007 (UTC)

This reminds me that the TI calculators (TI-83/84) and some text books (Key Math's Discovering Algebra pg 179) list intercept form as y=a+bx, I'd hope my students could figure it out if they visited this site, but I'm not sure. Is it worth mentioning? I don't know. Mrpalmer16 (talk) 21:08, 18 May 2008 (UTC)

[edit] Merge proposal

I suggest merging Linear equation and Linear function. I would prefer to merge to Linear function since it is easy to derive an equation from a function. —Celtic Minstrel (talk • contribs) 20:51, 6 December 2007 (UTC)

Probably better to merge it with System of linear equations. /Pieter Kuiper (talk) 10:04, 9 December 2007 (UTC)
I was a bit too fast there, reacting to the first figure, which shows two linear equations, not a system. /Pieter Kuiper (talk) 10:13, 9 December 2007 (UTC)