Is 4x-5y+2xy=0 linear or nonlinear? Explain.

Definitely nonlinear - this is because we are dealing with 3 variables, x, y and xy. If we just had x and y then it would be linear, but the xy makes the function have a vertical asymptote at 3.

Step-by-step explanation:

Non-linear

Step-by-step explanation:

This is because this cannot be written in standard form or slope-intercept. y and x cannot be multiplied together if the equation is linear.

4x - 5y + 2xy = 0

4x - y(5 - 2x) = 0

-y(5 - 2x) = -4x

-y = -4x / (5 - 2x)

y = 4x / (5 - 2x)

[when y is isolated to set a linear equation to slope-intercept, m is not constant, and there is no constant term]

This is a hyperbola and not a linear equation.

When y is isolated on the left side to set a linear equation to slope intercept, it must follow the form

y = mx + b.

Where m is the slope, b is the constant that is the y intercept.