Question 66874
The line you want will be perpendicular to the line 
through the points (-6,4) and (0,8), so you know that 
if y=mx + b is the equation of the line through
(-6,4) and (0,8), then the slope of the perpendicular is
-1/m. If it's midway between the points, you need to sind that 
midpoint.
First find the slope you want.
{{{(y - 4) / (x - (-6)) = (8 - 4) / (0 - (-6))}}} point-slope formula
{{{(y - 4) / (x + 6) = 4 / 6)}}}
{{{6*(y - 4) = 4*(x + 6)}}}
{{{3y - 12 = 2x + 12}}}
{{{3y = 2x + 24}}}
{{{y = (2/3)x + 8}}}
check this. Does this line go through (-6,4) and (0,8)?
{{{4 = (2/3)*(-6) + 8}}}
{{{4 = -4 + 8}}}
{{{4 = 4}}}
OK
{{{8 = (2/3)*0 + 8}}}
{{{8 = 8}}}
OK
The perpendicular line will have slope {{{- (1/(2/3)) = -(3/2)}}}
Now find midpoint between (-6,4) and (0,8)
{{{y[mid] = (8 + 4) / 2}}}
{{{y[mid] = 6}}}
{{{x[mid] = (-6 + 0) / 2}}}
{{{x[mid] = -3}}}
midpoint is (-3,6)
{{{(y - 6) / (x - (-3)) = -(3/2)}}}
{{{2*(y - 6) = (-3)*(x + 3)}}}
{{{2y - 12 = -3x - 9}}}
{{{y =  -(3/2)x + 3/2}}} answer
Does it go through (-3,6)?
{{{6 = -(3/2)*(-3) + 3/2}}}
{{{6 = 9/2 + 3/2}}}
{{{6 = 6}}}
OK