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# Coordinates

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

May 20, 2022

#1
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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!

May 20, 2022