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Learning about finding the slope of a line

  1. Mar 18, 2003 #1
    I just don't get it!

    We're learning about finding the slope of a line. And I don't get any of it, so can someone explain it to me? I could find the slope through a pair of points:

    C->1(2,1) 1-1 =0
    D->2(3,1) 2-3 =-1 and the answer is 0...(note that this is algebra((or pre-algebra)), not calculus)

    but when it comes to the graph, I'm not so sure. My guess would be to do the samething I did above? (there are multiple xy coordinates on the graphs in my text book).

  2. jcsd
  3. Mar 18, 2003 #2
    I'm sorry, what's your question? What a slope of 0 means graphically? Or the deal with the whole concept of slope in general?
  4. Mar 18, 2003 #3
    I meant to ask how to measure the slope on a graph.[?]
  5. Mar 18, 2003 #4
    To find the slope of a straight line through two coordinates find the change in the y-coordinate and divide by the change in x-coordinate. You'll probably need to be more specific....
  6. Mar 18, 2003 #5
    [sigh], I guess I'll try to ask my teacher
    (and he's not the best at explaining) ...i can't be specific on something I don't understand....
  7. Mar 18, 2003 #6
    Is my work(on my very first post on this thread) similar to what you're specifying?

    ***A spark of hope***
  8. Mar 18, 2003 #7
    Re: slopes!!??

    Actually I don't follow this notation...
    Can you explain what you have tried to do?
  9. Mar 18, 2003 #8
    Slope on a graph is rise over run. So if you've got a line that moves up three units every time you move over one unit in the positive x direction, then the slope will be the rise (3) over the run (1) = 3/1 = 3. That's a steeper slope than, say, a line that moves up one unit (rise) every time it moves over three units (run) in the positive x direction--this slope would be 1/3.

    Ugh, that was pretty nonmathematical sounding, huh?
  10. Mar 18, 2003 #9
    I GOT IT!! now for questions:

    is the run always 1?
  11. Mar 18, 2003 #10

    actually, the two notations are one. there was supposed to be
    a fraction bar seperating the notations.
  12. Mar 18, 2003 #11


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    No the run does not have to be 1, it is just easy to work with. If the slope is something like 3/5, that means up 3 when your run is 5, you could say the run is 2.5, and rise is 1.5. the key is that the ratio remains the same for a given line. That means a line has a constant slope. No matter where you measure it you will get the same result. No matter how big your run the RATIO of rise/run remains the same.
  13. Mar 18, 2003 #12
    can the slope be angular(consist of right angles in particular)?
  14. Mar 18, 2003 #13


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    Yes, to get the angle for rise over run, simply take arctan (rise/run)

    tangent is opposite side over adjacent side to the angle you are measuring. The opposite side is the rise, the adjacent side is the run.

    The right angles depend.

    If the angle is 0, that would correspond to a slope of 0.

    If the angle is 90, then the slope is undefined, because it is no longer a function (multiple values in y for a specific value x)
    Last edited: Mar 18, 2003
  15. Mar 19, 2003 #14


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    The "slope" of a line basically tells you how steep the line is.

    I tried drawing some lines as examples but the HTML yanks out spaces so it didn't work - sorry.

    The sign of a lines slopw indicates whether the line slopes up or down [ where up and down means starting at the left most part of the line and seeing if the point on the line moves upr or down as you move to the right]. A "+" sign means it slopes up and a "-" sign means it slopes down. If it has no slope (i.e. slope = 0) then it netier goes up nor down. Thus the line


    has zero slope. To measure the slope we look at a particular portion of the line - Then we use the "change in rise" and compare it to the "change in run" for that part of the line. And as you can see just by looking at a line it doesn't matter what part of the line or how much of the line you choose. To make this clear use the symbols

    dy = "Change in rise"
    dx = "Change in run"

    and define then as follows: For *any* two points A and B on the line A(X_a, Y_b) and B(X_b, Y_b) where A is a point to the left of B. By "to the left of B" I mean that we choose A as the one such that X_a < X_b. If X_a = X_b then the line is said to have infinite slope (infinite steepness).

    dx = X_b - X_a
    dy = Y_b - Y_a

    Then "define" the quantity "m" as the slope and it has the value

    m = dy/dx

    Play with it a bit and try using different points. If you have further questions I'd be more than happy to explain further.

  16. Mar 19, 2003 #15

    what is that equation for? I'm guessing is to measure an infinite slope?

    thanks a lot you guys!!

    now, for transversal slopes....I'm not sure what they are..I know what a transversal line is but not a transversal slope (are they the same?)
  17. Mar 19, 2003 #16

    so "arctan" means rise/run?

    OKAY,functions! I'm not 2 sure about them either (I don't have the best math teacher...):frown:
  18. Mar 19, 2003 #17

    Tom Mattson

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    As to m=dy/dx...

    No, that's for any slope. I'm guessing that pmb doesn't know how to make a "delta" in this forum (neither do I). It simply says that the slope (m) of a line is equal to the change in y over the change in x.

    No, "slope" means rise/run. "arctan(x)" is the inverse of tan(x). I seriously doubt that you need to worry about it.
  19. Mar 19, 2003 #18


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    dy = delta y = change in y = rise
    dx = delta x = change in x = run
    m = slope

    dx/dy = rise/run = slope = m

    That notation is generally not used until calculus though. And people here tend to have trouble lowering the level of their explanations (no offense, but it is a real problem and not just in here).

    The simplest way I can give you for slope between two points:


    (y2-y1)/(x2-x1) = slope

    On a graph, you can pick any points along the line, but its best to pick points that make the math as easy as possible. If the line starts at the origin (0,0) use that point for your first point.
  20. Mar 19, 2003 #19

    Why shouldn't I worry about it?
    what's tan(x)?
  21. Mar 19, 2003 #20
    You're in pre-algebra, correct? You won't need to know that for a while.
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