Find the Constant of Variation x/y=-6

$\frac{x}{y} = - 6$

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$y, 1$

The LCM of one and any expression is the expression.

$y$

Step 2

Multiply each term in $\frac{x}{y} = - 6$ by $y$ to eliminate the fractions.

Multiply each term in $\frac{x}{y} = - 6$ by $y$ .

$\frac{x}{y} y = - 6 y$

Simplify the left side.

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{x}{y} y = - 6 y$

Rewrite the expression.

$x = - 6 y$

Step 3

Solve the equation.

Rewrite the equation as $- 6 y = x$ .

$- 6 y = x$

Divide each term in $- 6 y = x$ by $- 6$ and simplify.

Divide each term in $- 6 y = x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{x}{- 6}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{x}{6}$

Step 4

Since the equation can be written in the form $y = k x$ , $y$ varies directly with $x$ and $k$ . The constant of variation, $k$ , is $- \frac{1}{6}$ .

$- \frac{1}{6}$

Find the Constant of Variation x/y=-6

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