Coordinates

In order to find k, you need to plug ($\frac{1}{4}$,-6) into the equation and solve for k.

-$\frac{1}{2}$ - kx = 6y

Plug in x and y (x,y)

-$\frac{1}{2}$ - k($\frac{1}{4}$) = 6(-6)

Simplify

-$\frac{1}{2}$ - $\frac{1}{4}$k = -36

Add $\frac{1}{2}$ to both sides

In order to do this, -36 turns into -$\frac{72}{2}$ 

-$\frac{1}{4}$k = -$\frac{71}{2}$

Divide each side by -$\frac{1}{4}$

This means it's actually being multiplied by -4: -$\frac{71}{2}$(-4)

k = $\frac{284}{2}$

Simplify

k = 142

Alternatively:

-$\frac{1}{4}$k = -35.5 instead of -$\frac{71}{2}$

Multiply by -4 on both sides

k = 142

It saves you the step of simplification, but some prefer to keep the fraction instead of switching to decimals. Figured I would show both!