Find the Constant of Variation 0.7x-1.4y=0

$0.7 x - 1.4 y = 0$

Step 1

Subtract $0.7 x$ from both sides of the equation.

$- 1.4 y = - 0.7 x$

Step 2

Divide each term in $- 1.4 y = - 0.7 x$ by $- 1.4$ and simplify.

Divide each term in $- 1.4 y = - 0.7 x$ by $- 1.4$ .

$\frac{- 1.4 y}{- 1.4} = \frac{- 0.7 x}{- 1.4}$

Simplify the left side.

Cancel the common factor of $- 1.4$ .

Cancel the common factor.

$\frac{- 1.4 y}{- 1.4} = \frac{- 0.7 x}{- 1.4}$

Divide $y$ by $1$ .

$y = \frac{- 0.7 x}{- 1.4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{(0.7) x}{1.4}$

Factor $0.7$ out of $0.7 x$ .

$y = \frac{0.7 (x)}{1.4}$

Factor $1.4$ out of $1.4$ .

$y = \frac{0.7 (x)}{1.4 (1)}$

Separate fractions.

$y = \frac{0.7}{1.4} \cdot \frac{x}{1}$

Divide $0.7$ by $1.4$ .

$y = 0.5 \frac{x}{1}$

Cancel the common factor of $0.5$ .

Factor $0.5$ out of $1$ .

$y = 0.5 \frac{x}{0.5 \cdot 2}$

Cancel the common factor.

$y = 0.5 \frac{x}{0.5 \cdot 2}$

Rewrite the expression.

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

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 $\frac{1}{2}$ .

$\frac{1}{2}$