is this a linear equation

No, it is non linear. Notice the xy term.

xy=2

Yes, the equation 4xy + 2y = 9 is a linear equation.

To confirm if an equation is linear, we need to check if it satisfies two conditions:
1. The variables are raised to the first power only (no exponents or radicals).
2. The variables are not multiplied or divided together.

In our equation, the variables x and y are raised to the first power, and there are no multiplication or division operations between them. Therefore, the equation is linear.