Determine if Linear x-7/y=0

$x - \frac{7}{y} = 0$

Step 1

Solve the equation for $y$ .

Subtract $x$ from both sides of the equation.

$- \frac{7}{y} = - x$

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 $- \frac{7}{y} = - x$ by $y$ to eliminate the fractions.

Multiply each term in $- \frac{7}{y} = - x$ by $y$ .

$- \frac{7}{y} y = - x y$

Simplify the left side.

Cancel the common factor of $y$ .

Move the leading negative in $- \frac{7}{y}$ into the numerator.

$\frac{- 7}{y} y = - x y$

Cancel the common factor.

$\frac{- 7}{y} y = - x y$

Rewrite the expression.

$- 7 = - x y$

Solve the equation.

Rewrite the equation as $- x y = - 7$ .

$- x y = - 7$

Divide each term in $- x y = - 7$ by $- 1 x$ and simplify.

Divide each term in $- x y = - 7$ by $- 1 x$ .

$\frac{- x y}{- 1 x} = \frac{- 7}{- 1 x}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x y}{x} = \frac{- 7}{- 1 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x y}{x} = \frac{- 7}{- 1 x}$

Divide $y$ by $1$ .

$y = \frac{- 7}{- 1 x}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{7}{x}$

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 x-7/y=0

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