Question 318876
Convert both equations to slope-intercept form,
{{{ax+3y=9}}}
{{{3y=-ax+9}}}
{{{y=-(a/3)x+3}}}
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{{{3x+y=-4}}}
{{{y=-3x-4}}}
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Perpendicular lines have slopes that are negative reciprocals,
{{{m1*m2=-1}}}
{{{-(a/3)*(-3)=-1}}}
{{{highlight(a=-1)}}}
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{{{drawing(300,300,-5,5,-5,5, grid(1),graph(300,300,-5,5,-5,5, -3x-4,x/3+3))}}}