Question 902096
Simplify your given equation!

{{{96x/6-24y/6-72/6=0}}}
{{{16x-4y-12=0}}}
{{{highlight_green(4x-y-3=0)}}}


{{{4x-y-3=0}}} can be solved for y.
{{{highlight_green(y=4x-3)}}}
Which is slope-intercept form for your given, now simplified, equation.


The line perpendicular to the given line will have slope {{{-(1/4)}}}, which is the negative
reciprocal of 4.  That is how perpendicular lines in a plane work.  The line you are looking
for is {{{y=-x/4+b}}}  and you do not yet know what is b.


Next, you want to know the midpoint of the two given points, because you are told that
{{{y=-x/4+b}}} must include this point.
MIDPOINT:   {{{x=(-22+14)/2=-4}}};  {{{y=(6+(-16))/2=-5}}}

This midpoint is (-4,-5).


You can solve the equation you want for b and use this found point (-4,-5) to get the value
of b.
{{{b=y-mx}}}
{{{b=y-(-1/4)x}}}
{{{b=-5-(-1/4)(-4)}}}
{{{b=-5-1}}}
{{{highlight_green(b=-6)}}}


Finish writing the equation asked for.
{{{highlight(y=-x/4-6)}}}