Determine if Linear 2/y=x

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

Step 1

Solve the equation for $y$ .

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.

$y$

Multiply each term in $\frac{2}{y} = x$ by $y$ to eliminate the fractions.

Multiply each term in $\frac{2}{y} = x$ by $y$ .

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

Simplify the left side.

Cancel the common factor of $y$ .

Cancel the common factor.

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

Rewrite the expression.

$2 = x y$

Solve the equation.

Rewrite the equation as $x y = 2$ .

$x y = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

Not Linear

Determine if Linear 2/y=x

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