Question

determine whether the equation 2x + 3y = 9xy represents a linear or nonlinear function. explain. the equation represents a function because it be written in the form y = mx + b.

Explanation:

Step1: Recall linear - function form

A linear function is of the form $y=mx + b$, where $m$ and $b$ are constants and there are no products of variables.

Step2: Try to rewrite the given equation

Starting with $2x + 3y=9xy$, we want to solve for $y$.
$3y-9xy=-2x$.
Factor out $y$: $y(3 - 9x)=-2x$.
Then $y=\frac{-2x}{3 - 9x}$. This cannot be written in the form $y = mx + b$.

Answer:

nonlinear; cannot