Find the Constant of Variation 9/y=x

$\frac{9}{y} = x$

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 $\frac{9}{y} = x$ by $y$ to eliminate the fractions.

Multiply each term in $\frac{9}{y} = x$ by $y$ .

$\frac{9}{y} y = x y$

Simplify the left side.

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{9}{y} y = x y$

Rewrite the expression.

$9 = x y$

Step 3

Solve the equation.

Rewrite the equation as $x y = 9$ .

$x y = 9$

Divide each term in $x y = 9$ by $x$ and simplify.

Divide each term in $x y = 9$ by $x$ .

$\frac{x y}{x} = \frac{9}{x}$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x y}{x} = \frac{9}{x}$

Divide $y$ by $1$ .

$y = \frac{9}{x}$

Step 4

The given equation $y = \frac{9}{x}$ can not be written as $y = k x$ , so $y$ doesn\'t vary directly with $x$ .

$y$ doesn\'t vary directly with $x$