Question 1004785
Standard Form for a line, Ax+By=C.


Slope based on the standard form equation is {{{-A/B}}}.  If you want to know this for sure, take the general standard form and solve for y in terms of x, and you'll see.  Your slope is  {{{2/3}}}.


Use the given point to compute the value for C.
{{{2x-3y=2*6-3*9}}}




ANOTHER WAY - USE POINT-SLOPE FORM
{{{y-9=(2/3)(x-6)}}}, simply substituting the given information into the form
{{{3y-27=2(x-6)}}}
{{{3y-27=2x-12}}}
{{{2x-12=3y-27}}}
{{{2x-3y=-27+12}}}
{{{2x-3y=-15}}}