Find the Constant of Variation 2x+6y=0

$2 x + 6 y = 0$

Step 1

Subtract $2 x$ from both sides of the equation.

$6 y = - 2 x$

Step 2

Divide each term in $6 y = - 2 x$ by $6$ and simplify.

Divide each term in $6 y = - 2 x$ by $6$ .

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2 x$ .

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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 $- \frac{1}{3}$ .

$- \frac{1}{3}$

Find the Constant of Variation 2x+6y=0

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