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 Is 3xy=6 a linear equation?

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user6595342 | eNotes Newbie

Posted October 31, 2013 at 6:04 PM via web

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 Is 3xy=6 a linear equation?

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flbyrne | (Level 3) Assistant Educator

Posted October 31, 2013 at 7:09 PM (Answer #1)

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Solving for y we get the function:


`y=2/x` or `y=2x^-1` , x is at the -1 power.

The general form of a linear equation is `ax+b=c`, or expressed as a function `y=ax+b` and the graph is a line. x is at the power of 1

In this case `y=2x` would be a linear equation.

See the graphs below:

`y=2x`  blue

`y=2/x` red

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flbyrne | (Level 3) Assistant Educator

Posted October 31, 2013 at 7:11 PM (Answer #2)

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The answer is: `3xy=6` is not a linear equation.

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michuraisin | Student, College Junior | (Level 1) Salutatorian

Posted October 31, 2013 at 9:18 PM (Answer #3)

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3xy=6 would not be a linear equation. Usually, a linear equation will follow the form y=mx+b. If we change your equation so we have it in terms of y, then it would be:

y=6/3x, or simplified to:


As you can see, that doesn't comply with y=mx+b.

Also, linear equations must produce linear lines on a graph. If we graph out y=2/x, we see that this is not the case.



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tonys538 | Student, Undergraduate | TA | (Level 1) Valedictorian

Posted September 29, 2014 at 4:01 AM (Answer #4)

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If y = f(x) represents a linear equation it can be written as y = ax  + b where a and b are constants.


y = 6/(3x)

y = 2/x

It can be seen that the value of y is not directly proportional to that of x, rather y and x are inversely proportional to each other. As the value of x increases, the value of y decreases and as the value of x decreases the value of y increases.

3*x*y = 6 is not a linear equation.

This is clearly shown in the graph of y versus x.

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