Question 323701
First find the line it's perpendicular to,
{{{x/3-y/9=1}}}
{{{y/9=x/3-1}}}
{{{y=3x-9}}}
This line has a slope of {{{m=3}}}
Perpendicular lines have slopes that are negative reciprocals,
{{{m1*m2=-1}}}
{{{3*m2=-1}}}
{{{m2=-1/3}}}
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Use the point-slope form of a line with point (-5,6) and slope (m=1/3)
{{{y-yp=m(x-xp)}}}
{{{y-6=(-1/3)(x-(-5))}}}
{{{y-6=-(1/3)x-5/3}}}
{{{highlight(y=-(1/3)x+13/3)}}}
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{{{drawing(300,300,-10,10,-10,10,grid(1),circle(3,0,.3),circle(0,-9,0.3),circle(-5,6,0.3),graph(300,300,-10,10,-10,10,3x-9,-(1/3)x+13/3))}}}