# 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!

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 $1$.
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!