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

2 Answers
Aug 2, 2018

Answer:

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.
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Aug 2, 2018

Answer:

#" "#
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:

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

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

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#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.