in short, the standard is just the same thing, expanded and with only the constant on the right-hand-side,
[tex]\bf \stackrel{point-slope~form}{y-1=\cfrac{1}{4}(x-12)}\implies y-1=\cfrac{1}{4}x-3\implies \stackrel{slope-intercept~form}{y=\cfrac{1}{4}x-2}
\\\\\\
\stackrel{standard~form}{-\cfrac{1}{4}x+y=-2}[/tex]
