# Is y= -4/x a linear equation?

Aug 2, 2018

The given equation is not linear because the power of $x$ is not 1 but - 1.

#### Explanation:

Given -

$y = - \frac{4}{x}$

The given equation is not linear because the power of $x$ is not 1 but - 1. Let us rewrite the equation as -

$y = - 4 {x}^{- 1}$

Look at this graph of the given equation.

Aug 2, 2018

$\text{ }$
No.

$y = - \frac{4}{x}$ is NOT a linear equation.

It is a reciprocal equation.

#### Explanation:

$\text{ }$
Given:

color(red)(y=f(x)=( -4/x)

Generate a data table as shown below:

Display just the color(red)(x and y columns for graphing:

Graph both the parent reciprocal function and the given function for the purpose of comparison:

$y = f \left(x\right) = \frac{1}{x}$

is a reciprocal function and it represents a hyperbola.

It is also an odd function.

The function's domain is all real values, except zero.

It is also very obvious, examining the graph:

For the parent function : $y = f \left(x\right) = \left(\frac{1}{x}\right)$

Horizontal and Vertical Asymptotes: color(red)(x=0 and y=0

For the given function : $y = f \left(x\right) = \left(- \frac{4}{x}\right)$

Horizontal and Vertical Asymptotes: color(red)(x=0 and y=0

Hope it helps.