Results 1 to 3 of 3

Math Help - Why is the difference in rise equal to the difference in run*slope?

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    Ohio
    Posts
    7

    Why is the difference in rise equal to the difference in run*slope?

    Point slope form: y - y1 = m(x - x1)

    I realize this is a manipulation of the slope equation: m = rise/run, but I don't understand what is happening or why it works. The difference in your y values is equal to the difference of your x values multiplied by the slope. I'm having trouble seeing this. I don't exactly understand what is going on here. How and why?

    I came to ask if someone could please clear this confusion up for me? I would really appreciate the help in understanding this!

    Please go slow with your explanation so I understand. x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,992
    Thanks
    1129

    Re: Why is the difference in rise equal to the difference in run*slope?

    You seem to know that "slope" is defined as m= rise/run. If you multiply both sides of that equation by "run" you get "rise= m*run". That is, because [tex]m= \frac{y_1- y_0}{x_1- x_0}[tex], multiplying both sides by x_1- x_0 you have y_1- y_0= m(x_1- x_0)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,403
    Thanks
    1486
    Awards
    1

    Re: Why is the difference in rise equal to the difference in run*slope?

    Quote Originally Posted by MiguelTime View Post
    Point slope form: y - y1 = m(x - x1)
    I realize this is a manipulation of the slope equation: m = rise/run, but I don't understand what is happening or why it works.

    I have never been a fan of that definition: the slope equation: m = rise/run.

    Now I understand why members of the mathematics education community invented it. But I don't find is useful.

    Given two points, the slope of the line they determine is the change is the second coordinates divided by the change is the first coordinates (provided the second is not zero).

    Examples: If P: (4,3)~\&~Q: (7,1) then the change is the second coordinates is -2 while the change is the first coordinates is 3 so that slope is \frac{-2}{3}.

    Now all other pairs of points on the line \overleftrightarrow {PQ} share that same ratio.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: June 29th 2011, 05:57 PM
  2. difference of abs value
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 20th 2010, 05:28 PM
  3. Sum and Difference
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: November 11th 2008, 02:51 PM
  4. difference between finite element/finite difference method
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: October 2nd 2008, 11:03 AM
  5. Difference
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 1st 2007, 07:16 PM

Search Tags


/mathhelpforum @mathhelpforum