"standard form" for a linear equation is
color(white)("XXX")color(red)Ax+color(blue)By=color(magenta)C
where
color(white)("XXX")color(red)A, color(blue)B, color(magenta)C are integers
color(white)("XXX")(and usually with the restriction that color(red)A>=0)
Given
color(white)("XXX")1/2x+1/2y=6
Multiplying everything by 2 converts the coefficients to integers:
color(white)("XXX")color(red)1x+color(blue)1y=color(magenta)(12)
Relating this back to the "standard form" we have
color(white)("XXX")color(red)A=color(red)1
color(white)("XXX")color(blue)B=color(blue)1 and
color(white)("XXX")color(magenta)C=color(magenta)(12)
