There are a few different standard forms for a line, let's assume we're after
[tex] ax + by = c[/tex]
Let's write
[tex] \frac 3{10} x - y = -3 [/tex]
That's already in standard form and we could stop. Or we could multiply by 10.
[tex] 3 x - 10 y = -30 [/tex]
We can bring the constant to the same side; some people prefer that as standard form:
[tex] 3x - 10 y + 30 = 0[/tex]
There's also slope intercept form,
[tex]y = \frac 3 {10} x + 3[/tex]
Plenty more forms where these comes from.
