Is This Considered a Linear Equation?

[bballwaterboy]

I know that linear equations have variables, which have a power no greater than one.

So, for example, 5x + 2 = 15 is linear, because the x is to the first power only.

But what about this equation:
x/x+2 = 80

This has an x in the denominator. Could we consider this linear still, because no x/variable is to a power greater than 1? Thanks!

 

[Mentallic]

Is that supposed to be x/(x+2) = 80? Because what you wrote would be interpreted as

$$\frac{x}{x}+2=80$$ which is not a true statement.

If it's the former, then no, it's not linear.

$$y=\frac{x}{x+2}$$ is what you'd call a rational function because it is comprised of a (linear) polynomial in the numerator and denominator.

 

[HallsofIvy]

As it is written, $$\frac{x}{x+ 2}= 80$$ it is not linear. But it can easily be converted to a linear equation:
x= 80(x+ 2)= 80x+ 160. Some texts call that an "equation of linear type" rather than a "linear equation".