Correct standard form for the equation of a line? So I was tutoring an Algebra 1 student yesterday and we were reviewing the three forms in which one can write the equation for a line: point-slope form, slope-intercept form and standard form. I told him to write an equation in standard form and he wrote:
$\frac x5 + \frac y4 = 1$ and I told him to rewrite it without any fractions as $4x +5y = 20$
Are both forms correct? I understand that the latter form may be more common but what I really want to know is if it is acceptable to use the former. Thanks all!
 A: I agree that the latter is more common, but the former is indeed acceptable: each describes precisely the same line, after all! 
However, I think it's perfectly reasonable to suggest that, when presenting the equation of a line in "standard form," to strive for integer coefficients.
A: The first form is usually called intercept form. That's because if you can write the equation in the form $\frac{x}{a} + \frac{y}{b} = 1$, then the $x$-intercept is $a$ and the $y$-intercept is $b$.
General form isn't unique, but intercept form is a specific variety of the general form in which the constant term is $1$ and is isolated on one side, and the coefficients of the variables are written as fractions with numerator $1$.
A: I have been taught that the standard form is: $$Ax + By + C = 0$$
Where A, B, and C are all integers, and A must be positive. So the latter part is correct.
For example, if I have a "messy" equation in slope-intercept form, $$y = x/2 + 3/4$$
I would have to multiply both sides by 4, giving me the equation: $$4y = 2x + 3$$
Because the coefficient of the x term has to be positive, I will move 4y to the right, which gives: $$2x - 4y + 3 = 0$$
I hope this answer helped! 
