Question 842864
The closest point is a perpendicular line containing the point.
The line perpendicular to {{{-3x+4y+3=0}}} or {{{y=(3x-3)/4}}} has a slope of 
{{{(3/4)*m=-1}}}
{{{m=-4/3}}}
{{{y=-(4/3)x+b}}}
Use the point to solve for {{{b}}}
{{{-5=-(4/3)(1)+b}}}
{{{-15/3+4/3=b}}}
{{{b=-11/3}}}
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{{{y=-(4/3)x-11/3}}}
{{{3y=-4x-11}}}
{{{highlight(4x+3y+11=0)}}}
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{{{drawing(300,300,-5,5,-8,2,grid(1),circle(1,-5,0.2),
graph(300,300,-5,5,-8,2,-(4/3)x-11/3,(3x-3)/4))}}}