Question

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

Answer 1

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

Explanation:

Given -

`y=-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=-4x^(-1)`

Look at this graph of the given equation.

Answer 2

`" "`
No.

`y= -4/x` is NOT a linear equation.

It is a reciprocal equation.

Explanation:

`" "`
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(x)=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(x)=(1/x)`

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

For the given function : `y=f(x)=(-4/x)`

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

Hope it helps.