SOLUTION: Determine K for the following two lines are parallel. {{{(k-2)x - ky + pi = 0}}} {{{5x + 7y + sqrt(7) = 0}}}

Algebra ->  Graphs -> SOLUTION: Determine K for the following two lines are parallel. {{{(k-2)x - ky + pi = 0}}} {{{5x + 7y + sqrt(7) = 0}}}      Log On


   

Question 547278: Determine K for the following two lines are parallel.
%28k-2%29x+-+ky+%2B+pi+=+0
5x+%2B+7y+%2B+sqrt%287%29+=+0
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
remember that if two lines are parallel, they have the same slope (m value in y=mx+b)
We need to get both of the lines into our slope-intercept form (y=mx+b).
%28k-2%29x+-+ky+%2B+pi+=+0
%28k-2%29x%2Bpi=ky
y=%28k-2%29%2Fk%2Ax%2Bpi%2Fk



5x+%2B+7y+%2B+sqrt%287%29+=+0
7y=-5x-sqrt%287%29
y=-5%2F7%2Ax-sqrt%287%29%2F7
If these lines are parallel, this means that the two m values are equal:
%28k-2%29%2Fk=5%2F7
This means that:
k-2=5+-%3E+k=7
and
k=7
(this was just by equating both the numerators and both the denominators).
Both of these equations show that k=7