Question 359089
{{{x+4y+8=0 }}}
Convert to slope-intercept form, {{{y=mx+b}}}
{{{4y=-x-8}}}
{{{y=-(1/4)x-2}}}
Slope:{{{m=-1/4}}}
Perpendicular lines have slopes that are negative reciprocals,
{{{m[1]*m[2]=-1}}}
{{{-(1/4)*m[2]=-1}}}
{{{m[2]=4}}}
Use the slope-intercept form,
{{{y=4x+b}}} 
Use the point to solve for {{{b}}}.
{{{-2=4(3)+b}}}
{{{b=-2-12}}}
{{{b=-14}}}
Complete the calculation to get {{{b}}}, then put it all together, to get the equation of the perpendicular line.
{{{y=4x-14}}}
.
.
.

{{{drawing(300,300,-2,8,-8,2,circle(3,-2,0.18),grid(1),graph(300,300,-2,8,-8,2,-(1/4)x-2,4x-14))}}}