Standard form: ax+by=c or ax+by+c=0? is y-first okay?

I gave seen standard form defined as ax+by=c. And ax+by+c=0

which is correct?
and is if ok if the y is written first (by+ax=c)
thank you

Mo11 said:

I gave seen standard form defined as ax+by=c OR ax+by+c=0
which is correct?

Click to expand...

Either is correct. Each is convenient for different purposes.
The slope \(\displaystyle \dfrac{-a}{b}\) can be read or used easily from either.
The first is convenient for dealing with \(\displaystyle x~\&~y\) intercepts: \(\displaystyle x_0=\dfrac{c}{a}~\&~y_0=\dfrac{c}{b}\).
The second is useful for distance from a point \(\displaystyle (p,q)\) to that line: \(\displaystyle \dfrac{|a~p+b~q+c|}{\sqrt{a^2+b^2}}\)

Mo11 said:

I gave seen standard form defined as ax+by=c. And ax+by+c=0

which is correct?

Click to expand...

Ironically, there is no standard definition for the "standard form" for the equation of a straight line. The "correct" form is whatever your particular textbook or particular instructor wants, at a particular time, in a particular course. Next semester, the definition may change.

Your best bet is to ask your instructor, specifically, for what s/he'll want on the upcoming test. (And this is why better instructors refer to "point-slope form", "slope-intercept form", etc, rather than to "standard form"!)