# Is 3xy=6 a linear equation?

flbyrne | Certified Educator

calendarEducator since 2013

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

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flbyrne | Certified Educator

calendarEducator since 2013

starTop subjects are Math, Science, and Arts

Solving for y we get the function:

`y=6/(3x)`

`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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tonys538 | Student

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

3*x*y=6

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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michuraisin | Student

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:

y=2/x

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.