First we find the slope of the line whose equation is

     

by solving it for y to get it in the form y=mx+b

           

Divide ever term through by -24

              
              
Compare that to y=mx+b and we see that m=4 and b=-3. We only need
the slope 4.  We don't need the y-intercept.

Any line perpendicular to a line whose slope is 4, has a slope which
is the reciprocal of 4 with the sign changed.  Therefore the slope
of the desired line will have slope .

Now we use the midpoint formula to find the midpoint between (-22,6) and
(14,-16)


Midpoint = 

where (x1,y1) = (-22,6)
and where (x2,y2) = (14,-16)

Midpoint = 

Midpoint = 

Midpoint = (-4,-5)

Next we use the point slope formula:


y - y1 = m(x - x1)
where m= and (x1,y1) = (-4,-5)

y - (-5) = 

y + 5 = (x + 4)

y + 5 = x - 1

    y = x + 6

Edwin