SOLUTION: A line passing through (5,-8) and (9,y) is perpendicular to a line with slope -4/9. Find the value of y.

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Question 79984: A line passing through (5,-8) and (9,y) is perpendicular to a line with slope -4/9. Find the value of y.
Answer by ankor@dixie-net.com(12689) About Me  (Show Source):
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A line passing through (5,-8) and (9,y) is perpendicular to a line with slope -4/9. Find the value of y.
:
Let m1 = (-4/9)
:
Find the slope m2 from the given coordinates; x1=5, y1=-8; x2=9; y2=y:
m2 = %28%28y+-+%28-8%29%29%29%2F%28%289+-+5%29%29 = %28%28y%2B8%29%29%2F4
:
We know the slope relationship of perpendicular lines is: m1 * m2 = -1
Substitute for m1 and m2:
:
%28-4%2F9%29%2A%28%28y%2B8%29%2F4%29 = -1
:
Conveniently, the 4's cancel so we have:
-%28%28y%2B8%29%2F9%29 = -1
:
%28%28y%2B8%29%2F9%29 = +1; multiplied by -1
:
y + 8 = 9; multiplied equation by 9
:
y = 9 -8
:
y = 1
:
Therefore m2 = %28%28y%2B8%29%29%2F4 = %28%281%2B8%29%29%2F4 = 9%2F4