Question 349533
Convert both lines to slope intercept form, {{{y=mx+b}}}.
{{{3x+ky=-4 }}}
{{{ky=3x+4}}}
{{{y=(3/k)x+4/k}}}
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{{{3x-y=7}}} 
{{{y=3x-7}}}
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Perpendicular lines have slopes that are negative reciprocals,
{{{m[1]*m[2]=-1}}}
Substituting,
{{{(3/k)(3)=-1}}}
{{{highlight(k=-9)}}}
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{{{graph(300,300,-10,10,-10,10,3x-7,-(1/3)x-4/9)}}}