Question 1200253
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Rule: Any two perpendicular lines, where neither is vertical nor horizontal, will have their slopes multiply to -1.


The slope through (-6,4) and (-2,5) is 1/4, which you correctly calculated.


The slope through (-3,4) and (0,k) is (k-4)/3, which you correctly calculated.


Multiply those slopes and set the product equal to -1.
slope1*slope2 = -1
(1/4)*(k-4)/3 = -1
(k-4)/12 = -1
k-4 = -1*12
k-4 = -12
k = -12+4
k = <font color=red size=4>-8</font> is the final answer.


Check:
Compute the slope of the line through (-3,4) and (0,-8)
m = (y2-y1)/(x2-x1)
m = (-8-4)/(0-(-3))
m = (-8-4)/(0+3)
m = -12/3
m = -4
This slope of -4 must multiply with the other slope of 1/4 to get a product of -1.
Sure enough (1/4)*(-4) = -1 is indeed the case. 
The answer has been verified.
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