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Nature of the standard form

  1. Aug 7, 2008 #1
    Why is the standard form of a linear equation ax + by = c? What is the significance of this particular way of writing the equation that makes it "standard"? When we graph a line, we always transform the equation into something else, such as the point-slope form, y = mx + b.

    In other words, what is the equation, without transformation, used for?
  2. jcsd
  3. Aug 7, 2008 #2
    Well I've always been told that it's for presentation purposes. But then again I view that equation as more of a diophantine equation anyways.
  4. Aug 8, 2008 #3
    I'm guessing a sorted polynomial form makes it easier to read and factor the thing? It doesn't really matter for a linear equation, but once you get higher degrees it does make a difference.

    A quick glance at the first factor tells you the degree, you can easily locate the constant, you can quickly see if it is a complete square. If it was written as a slope, some of those would take longer.

  5. Aug 8, 2008 #4


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    One advantage of that form is that every line can be written in that form. A vertical line, say one in which x is always 3, has the form x= 3, of course, which is ax+ by= c with a= 1, b=0, c= 3. It cannot be written in the form y= mx+ b because solving ax+ by= c for y involves dividing by b which, here, is 0. Additionally, in y= mx+ b y is necessairily a function of x. If x= 3, that is not true.
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