For what value of k are the lines 2x + 3y = 4k and x - 2ky = 7 parallel? Express your answer as a common fraction.

Put the equations into    y = mx + b     form     m = slope    if  m is the same in both equations, they are parallel

First one

2x + 3y = 4k

3y = -2x + 4k

y = -2/3 x + 4/3 k

 

Second one

x - 2ky=7

2ky = x-7

y = 1/(2k) x  - 1/(2k) *7

 

Now for the lines to be parallel     -2/3 = 1/(2k)      solve for 'k'