SOLUTION: The lines with equations 5x+3y=4 and 2kx-5y=10 are perpendicular. what is the value of k?

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Question 911953: The lines with equations 5x+3y=4 and 2kx-5y=10 are perpendicular. what is the value of k?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The lines with equations 5x+3y=4 and 2kx-5y=10 are perpendicular
what is the value of k?
:
Put both equations in the slope intercept form
5x + 3y = 4
3y = -5x + 4
y = -5%2F3x + 4%2Fx
:
2kx - 5y = 10
-5y = -2ks + 2
Divide both sides by -5
y = 2k%2F5x - 2
:
The slope relationship of perpendicular lines: m1 * m2 = -1, therefore:
-5%2F3 * 2k%2F5 = -1
%28-10k%29%2F15 = -1
multiply both sides by 15
-10k = -15
k = -15/-10
k = +1.5
Therefore the 2nd equation:
y = %282%2A1.5%29%2F5x - 2
y = 3%2F5x - 2
:
;
See if the relationship between the two slopes is -1
-5%2F3 * 3%2F5 = -1