Final answer:
The equation 4x ²+y=4 does not have a constant rate of change because it represents a parabolic curve, and the rate of change varies with different values of x.
Step-by-step explanation:
The equation given, 4x ²+y=4, is a parabolic equation, which describes a curve rather than a straight line. The rate of change in such equations is not constant because as x changes, the change in y is not uniform across all values of x, particularly in a parabolic equation where the rate of change is related to the derivative of the curve at a particular point.
A constant rate of change is typically found in linear relationships, where the equation is of the first order, i.e., the highest power of x is 1. For example, in the equation y = mx + b, m represents the constant rate of change or slope of the line. Since the equation in the question is a second-order polynomial (the highest power of x is 2), the rate of change is not constant but varies depending on the value of x.