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General form vs Standard form of a line

  1. Oct 2, 2012 #1
    I'm in the middle of a calculus course (this is not a calculus question per se), studying from the Larson text, and when an answer to a problem is the equation of a line, I solve for Standard form of a line [itex]Ax + By = C[/itex].

    I noticed, however, that the Larson textbook frequently terms answers of the equation of a line in the form [itex]Ax + By + C = 0[/itex], which apparently is the General form (based on my searching around on line. This answer is frequently the equation of a line tangent to a given point on a curve, if that is of any interest.

    What are the advantages of one form over another? Should I be using General when doing calculus for some reason? Thanks!
  2. jcsd
  3. Oct 2, 2012 #2


    Staff: Mentor

    I don't see much of an advantage for either form over the other. The first form is slightly more useful for graphing, although the slope-intercept form is probably better yet for nonvertical lines.

    The second (general) form has a counterpart with terms up through the second degree, for the conic sections, so maybe that's a motivation for this form.

    Overall, the distinctions between standard form and general form here aren't very important, IMO.
  4. Oct 3, 2012 #3
    What form is the most appropriate to use depends upon what you want to do with this equation.

    if you have two expressions of the type f(x,y) = 0 and g(x,y) = 0 you can equate them directly.

    If f(x,y) = a and g(x,y) = b then you cannot do this so easily.

    For calculus (and many other purposes) I would think that the intercept form of the line is more useful viz

    y = mx + b

    Since calculus is about slopes and m is the slope.

    go well
  5. Oct 4, 2012 #4
    Thank you both; that sort of makes sense. I always made use of the slope-intercept form ([itex]y=mx+b[/itex] fairly consistently as well. It just seems to be the most useful of all of the forms. Also, I was very lazy in grade school (decades ago), so -- while I have always had a strong aptitude and love of math -- there are some very interesting gaps in the some of the finer details of things I technically should know lol (like I am actually even relearning how to work with Standard form).

    I know Larson is far from the consummate text on calculus, but I figured the authors must have had some motivation for drafting answers in the way that they did. Thanks.
  6. Oct 4, 2012 #5


    User Avatar
    Science Advisor

    Hey lordofpi and welcome to the forums.

    The second form is typically the form of the equation of an n-dimensional linear object (also an n-dimensional plane) and it has the same form of n . (r - r0) = 0 for an n-dimensional vectors n, r, and r0 (all have to be the same size, but that size is variable).

    In a linear context, this can be useful depending on what you are trying to do.
  7. Oct 4, 2012 #6
    Thanks chiro for the additional info. And thank you: this place seems to pickup where Usenet left off all those years ago (plus Usenet never had [itex]\LaTeX[/itex]!). I am very excited to be able to participate in the ongoing conversations of so many sharp minds.
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