SOLUTION: A line has an equation of x + 5y - 4 = 0. If the line x - ky - 17 = 0 makes an angle of 45 degrees counter-clockwise from the line x + 5y

SOLUTION: A line has an equation of x + 5y - 4 = 0. If the line x - ky - 17 = 0 makes an angle of 45 degrees counter-clockwise from the line x + 5y - 4 = 0, find the value of k.

Question 1179238: A line has an equation of x + 5y - 4 = 0. If the line x - ky - 17 = 0 makes an angle of 45 degrees counter-clockwise from the line x + 5y - 4 = 0, find
the value of k.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x - ky - 17 = 0 makes an angle of 45 degrees counter-clockwise from the line x + 5y - 4 = 0
one line is 5y=-x+4
y = -x/5 +4/5 slope = -(1/5)
Other line x-ky -17=0
ky=x-17
y= x/k =17/k
slopes are (-1/5) , (1/k)

m1-m2= (1/k -(-1/5))
= (k+5)/5k------------N
1+m1m2 = 1+ (-1/5k) = (5k-1)/5k-----------D

N/D =1 = ((k+5)/5k) / ((5k-1)/5k))
1= k+5/ 5k-1
5k-1= k+5
4k =6
k=2/3

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