Question 364877
First find the slope of the line.
Convert to slope-intercept form, {{{y=mx+b}}, where {{{m}}} is the slope.
{{{4x-12y=6}}}
{{{12y=4x-6}}}
{{{y=(1/3)x-1/2}}}
{{{m[1]=1/3}}}
Perpendicular lines have slopes that are negative reciprocals.
{{{m[1]*m[2]=-1}}}
{{{(1/3)*m[2]=-1}}}
{{{m[2]=-3}}}
So the new line has the form,
{{{y=-3x+b}}}
Use the point (8,-5) to solve for {{{b}}},
{{{-5=-3(8)+b}}}
{{{-5=-24+b}}}
{{{b=24-5}}}
{{{b=19}}}
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{{{highlight(y=-3x+19)}}}
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{{{drawing(300,300,-2,10,-8,4,grid(1),circle(8,-5,0.3),graph(300,300,-2,10,-8,4,0,(1/3)x-1/2,-3x+19))}}}