To check if a point lies on a line, I can plug in the coordinates of the point into the equation of the line and see if it satisfies it. So I will substitute $x = \frac{1}{4}$ and $y = -6$ into the given equation and see what value of $k$ makes it true. If I do that, I get $-\frac{1}{2}-2k\left(\frac{1}{4}\right) = 5(-6)$. Simplifying, I get $-\frac{1}{2}-\frac{k}{2} = -30$. Multiplying both sides by 2, I get $-1-k = -60$. Adding 1 to both sides, I get $-k = -59$. Dividing both sides by -1, I get $k = 59$. This is the value of $k$ that makes the point $\left(\frac{1}{4},-6\right)$ lie on the line. 
For what value of $k$ does the line represented by the equation $-\frac{1}{2}-2kx = 5y$ contain the point $\left(\frac{1}{4},-6\right)$?