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!