For what value of k does the line represented by the equation-1/2 - kx = 6y contain the point (1/4,-6)?
+1975 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!
