Question 830606
Standard Form:  Ax+By=C

Slope-Intercept Form:  y=mx+b


Your given equation, 7x=3y-12, is not in either form.  It may represent a step from standard form toward solving for y:
7x-3y=-12   ------ standard form
7x=3x-12  ------ added -3x to both sides.


Changing from standard form to slope-intercept form can go this way:
THESE ARE THE STEPS!
{{{Ax+By=C}}}----Beginning in standard form
{{{By=C-Ax}}}
{{{By=-Ax+C}}}
{{{y=-(A/B)x+C/B}}}------Finishing in slope-intercept form
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The slope is {{{-(A/B)}}} and the y-intercept is {{{C/B}}}.