Question 943940
SLOPE OF AB  LINE
{{{(2-4)/(5-(-1))}}}
{{{-2/6}}}
{{{-1/3}}}


The requested line being parallel to AB will also have slope {{{-1/3}}}.



POINT-SLOPE EQUATION CONTAINING POINT C
{{{y-(-5)=-1/3(x-6)}}}
simplify
{{{y+5=-x/3+1/18}}}
and you can put the form into what you want.
{{{y=-x/3+1/18-5}}}
{{{3y=-x+1/6-15}}}
{{{3y+x=1/6-15}}}
{{{18y+6x=1-30}}}
{{{highlight(6x+18y=-29)}}} as standard form.