Find the Constant of Variation 4x=-6y

$4 x = - 6 y$

Step 1

Rewrite the equation as $- 6 y = 4 x$ .

$- 6 y = 4 x$

Step 2

Divide each term in $- 6 y = 4 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 4 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{4 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{4 x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{4 x}{- 6}$

Simplify the right side.

Cancel the common factor of $4$ and $- 6$ .

Factor $2$ out of $4 x$ .

$y = \frac{2 (2 x)}{- 6}$

Cancel the common factors.

Factor $2$ out of $- 6$ .

$y = \frac{2 (2 x)}{2 (- 3)}$

Cancel the common factor.

$y = \frac{2 (2 x)}{2 \cdot - 3}$

Rewrite the expression.

$y = \frac{2 x}{- 3}$

Move the negative in front of the fraction.

$y = - \frac{2 x}{3}$

Step 3

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 $- \frac{2}{3}$ .

$- \frac{2}{3}$

Find the Constant of Variation 4x=-6y

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