Perhaps the Best Resource Is....
For the past seven years on this website, I have been suggesting resources of all types. The one resource I have forgotten or ignored is the close presence of a colleague or peer. Very often, they can shed a helpful prospective on your question or concern.
Too illustrate, consider the following email request from a local mathematics teacher...
I have a math question that I hope you can help me with. I have researched this topic but have not found an answer I am satisfied with in the textbooks or online.
Well, I guess it is two questions:
 Why is the coefficient of the A term positive in the standard form of a linear equation?
 Why can't we have fractions in the standard form of a linear equation?
I found that the standard form is helpful for graphing the xand yintercepts of an equation, for solving systems of equations, and is necessary to write the equation of a vertical line, but I still can't figure out why there are no negative A values or fractions allowed. The best I can come up with is that the equations look nicer, and are easier to deal with when finding the xand yintercepts, but that can't be correct because that's just aesthetics.
Do you have any ideas or places I could look to find this answer?
How would you respond to this question? Part of the importance of the question lies in a need to understand (and possibly support) a textbook convention, while also perhaps being consistent with how other math teachers (at least in your school/district) teach forms of linear equations....let alone performance tests that match state requirements.
And finally, the example continues below with the email response from a colleague to the posed questions/concerns. Do you agree or disagree...or have something else to add to the situation?
As to your question, your hunch is basically right. There are no mathematical reasons for A being positive or lack of fractions as parameter coefficients. It is nothing more than convention....and if not followed, nothing dire happens (i.e. the math cops do not appear!)...except.... Some thoughts:
 Too many high school texts go further and state that A,B, C must be integers (see problem below with this restriction).
 Given form Ax+By=C, if A was negative, all one needs to do is multiply both sides by 1 to make A positive.
 If fractions occurred as coefficients, all one needs to do is multiply by LCM of all divisors and situation is corrected.
 BUT...what is the standard form of a horizontal line....such as y = 4. Then, A = 0, which is not positive....so, one needs to go back and say that A must be a positive integer OR zero.
 All of this sounds good, but the "true" definition has none of these requirements: "Ax+By=C where A and B are not both zero." [taken from James & James Mathematics Dictionary]
 Note that this "true" definition allows for case of horizontal line y = 4.
 Historically, the rules you mention were not in place....and algebra developed just fine.
 And lastly, the rules you mention can lead to complications. Suppose you start with a point slope form: y = (pi)x, which is a linear equation, producing a line with slope pi and yintercept of 0. Under your rule restrictions, it is impossible to produce a Standard Form for it....as dividing by pi creates a bigger mess, yet pi is not really a fraction, yet it is not an integer.
 But, one might say...the previous example is a weird case that can be avoided...and I say, no way....as it happens to be the famous C=(pi)D, which is the linear equation relating circumference and diameter.
My suggestion....ignore the rule and nothing will happen, other than perhaps a discussion about arbitrary conventions.
