Final answer:
The equation y=x(2-x) is a non-linear function because it expands to y=2x-x^2, which includes an x^2 term indicating that it represents a parabola.
Step-by-step explanation:
The equation y=x(2-x) does not represent a linear function because when expanded, it takes the form y = 2x - x^2. A linear equation is one that can be written in the standard form y = a + bx, where a is the y-intercept and b is the slope. In this case, because the equation includes an x^2 term, it represents a quadratic function, specifically a parabola, which is inherently non-linear. This means that the graph of this equation will not be a straight line but rather a curved line, typically opening either upwards or downwards depending on the sign of the x^2 term. In our case, since the x^2 term is negative, the graph would open downwards.