1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Nature standard form Date
Natural logarithm Jan 23, 2018
What's the standard deviation of values in the histogram bar Nov 17, 2017
Natural number question Jan 14, 2017
2017 times a is a natural number Dec 16, 2016
Natural Log Proof Oct 22, 2016