Talk:Slope
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[edit] Slope-point formula
the equation for the slope-point formula seems to have some kind of error at the end: it shows up as "y - y0 = m(x - x0)-". The source does not seem to have a '-' in the end, no clue where it's comming from.- AndreyF
- I know the m stands for slope in the formula... But why did they use the letter m? This is an extra credit problem on my homework.. If anyone knows, please tell me :) --anon
It is the first letter in the word for slope in the mathematician's language. Or at least that's what I learned. Jamesr66a 19:53, 19 March 2007 (UTC)
[edit] Slope and gradient -- request for comment
I thought the slope was exclusively about a line y=ax+b in the plane, and nothing else. Then the recently inserted paragraph is probably not very accurate. Oleg Alexandrov 15:44, 11 Mar 2005 (UTC)
[edit] Nitpicky semantics
The article currently says: The slope of a vertical line is not defined (it does not make sense to define it as +∞, because it might just as well be defined as -∞).
This isn't really an explanation of why it isn't defined. Is the (ambiguous) square root of 4 not defined since it could be 2 or -2? Of course not, its just both. Similarly, is 90 degrees not defined because it could just as well be 360+90? Even more similarly, is saying that one line is 90 degrees from another 'senseless' because it could also be 270 degrees? I'm sure there is a good way of explaining why we don't define it, but just saying 'because it could also be this' isn't really valid. --Intangir 20:47, 2 January 2006 (UTC)
- I guess the slope of a vertical line cannot be defined in any meaningful way.
- The slope is +∞ or −∞ depending on whether you travel on that vertical line up or down. Tricky business. :) Oleg Alexandrov (talk) 00:50, 3 January 2006 (UTC)
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- The fact that both work doesn't make it unmeaningful. +∞ slope means vertical line as does −∞. The things which are unmeaningful are like 0/0 or ∞/∞. Those things are unmeaningful because they could mean any number. Thats why we don't define them. However, a positive infinite slope has one meaning. It just so happens that it has the same meaning as negative infinite slope. The more I think about it, the more it seems that there is no reason for leaving a vertical slope undefined. --Intangir 02:03, 3 January 2006 (UTC)
- Would you please provide references for defining the vertical slope? I don't think the concept is standard (neither useful for that matter) and I would not agree with including such a thing without references. Thanks. Oleg Alexandrov (talk) 02:27, 3 January 2006 (UTC)
- The fact that both work doesn't make it unmeaningful. +∞ slope means vertical line as does −∞. The things which are unmeaningful are like 0/0 or ∞/∞. Those things are unmeaningful because they could mean any number. Thats why we don't define them. However, a positive infinite slope has one meaning. It just so happens that it has the same meaning as negative infinite slope. The more I think about it, the more it seems that there is no reason for leaving a vertical slope undefined. --Intangir 02:03, 3 January 2006 (UTC)
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- Sure, I found one from Math Forum and also this random quiz as well as this example of the concept applied usefully to programming. The math forum answer clearly points out that there is no real number slope for a vertical line. Hence if you require the slope to be a real number, one is out of luck since ∞ is not real, duh. But it would be a silly justification indeed to say that there is no such thing as an infinite slope because infinity is not defined for reals. Under a simple compactification of the reals like the extended real number line or the real projective line there is no trouble. Also, I don't see how saying that 'all lines except vertical ones have slope' is more useful than just allowing for infinite slope. There is no reason to be afraid of infinity here. An infinite slope behaves correctly. Consider the line y=∞x+b. Its reflection across the y axis is the same as for every other line y=-mx+b. In this case either itself, y=∞x+b or y=−∞x+b depending on which compactification is used. Its reflection about the line y=x is still y=x/m+b or y=x/∞+b ,ie y=0x+b. Certainly there is nothing unuseful about a vertical slope if it behaves exactly as it should. Furthermore, it is useful because it allows every line to be written
in slope intercept form.--Intangir 04:20, 3 January 2006 (UTC)- Errata- vertical lines don't all have a y-intercept, so some of them can't be expressed in slope-intercept form no matter what. However, every line can be written in point-slope form iff unbounded slopes are allowed.
- Sure, I found one from Math Forum and also this random quiz as well as this example of the concept applied usefully to programming. The math forum answer clearly points out that there is no real number slope for a vertical line. Hence if you require the slope to be a real number, one is out of luck since ∞ is not real, duh. But it would be a silly justification indeed to say that there is no such thing as an infinite slope because infinity is not defined for reals. Under a simple compactification of the reals like the extended real number line or the real projective line there is no trouble. Also, I don't see how saying that 'all lines except vertical ones have slope' is more useful than just allowing for infinite slope. There is no reason to be afraid of infinity here. An infinite slope behaves correctly. Consider the line y=∞x+b. Its reflection across the y axis is the same as for every other line y=-mx+b. In this case either itself, y=∞x+b or y=−∞x+b depending on which compactification is used. Its reflection about the line y=x is still y=x/m+b or y=x/∞+b ,ie y=0x+b. Certainly there is nothing unuseful about a vertical slope if it behaves exactly as it should. Furthermore, it is useful because it allows every line to be written
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I am not really impressed by the references provided. :) I would like a calculus book, or mathworld, or something more serious :) . But OK, I see your point. I would agree with a remark, or a section, or subsection somewhere in the article discussiong the concept. But I would not agree in putting that front and center in the introduction or something. I've been teaching math at college level for the last 6 years and never had to deal with infinite slope. :) So I don't know how important the concept is. Cheers, Oleg Alexandrov (talk) 05:27, 3 January 2006 (UTC)
The issue is not whether a vertical line should be defined as having infinite slope, but whether it is defined that way, which would require an authoritative reference, none of the above suffice. Paul August ☎ 05:36, 3 January 2006 (UTC)
Actually, the original issue was whether or not the reason given for why vertical lines have no slope makes sense. It seems it doesn't, no one is suggesting that it does, so I'm going to reword it. This is a matter of incoherence, not a matter of authority or existance. Of course, I might also like to make some statement affirming the sanity and utility of 'infinite slope'. However, I won't unless I can find a reputable enough source which uses it. If there isn't such a source then I agree that the article doesn't need to waste space talking about an unused concept. --Intangir 14:30, 3 January 2006 (UTC)
- All I've found is information on projective geometry and infinite slopes. However, I don't really care about the one point compactification very much at the moment, so I'm not going to bother writing a section on infinite slopes. As a final thought, the statement that y=∞x is the same as y=−∞x definitely does not imply that unbounded slopes are meaningless. The irrelevance of sign is just the insight that a vertical line is the one kind of line which can be thought of as both sloping down and sloping up. --Intangir 16:17, 3 January 2006 (UTC)
[edit] slope
I have seen the term "angular coefficient" used for "slope" (e.g. in nuclear physics). Should that be mentioned in the definition?
[edit] M?
My teacher asked me, and I) am wondering, why is M used to represent slope? Billvoltage 19:54, 29 September 2006 (UTC)
[edit] Why Calculus is Necessary
I'm confused about why the section is called that, or why there's a section separation at all —The preceding unsigned comment was added by 128.239.146.209 (talk • contribs) 03:09, 9 October 2006 (UTC)
- That makes sense to me - I went ahead and deleted the section header. Next time, you can feel free to be bold and do it yourself! (ESkog)(Talk) 03:20, 9 October 2006 (UTC)
[edit] 0 or undefined
I cannot understan why it changes if the line's vertical or horizontal. The slope is either 0 or undefined. --Unsigned by User:AgentPeppermint at 11:02, 22 November 2006
