Final Answer:
The rate of change of the equation x = -5 is 0, as it represents a vertical line with no slope.
Step-by-step explanation:
The equation x = -5 represents a vertical line passing through the point (-5, y) for all y. Since the slope of a vertical line is undefined, the rate of change, or the derivative, of x with respect to y is 0. This can be understood by considering that for any change in y, there is no corresponding change in x, as x always remains at -5. Mathematically, the derivative of x with respect to y is represented as dx/dy, and in this case, it equals 0.
In calculus, the rate of change or derivative measures how a function changes as its input changes. For the equation x = -5, there is no change in x for any change in y, indicating that the rate of change is 0. Graphically, this can be visualized as a vertical line on the coordinate plane where x always remains at -5 regardless of the value of y.
Understanding the concept of rate of change and its application to specific equations is fundamental in calculus and mathematical modeling. In this case, the equation x = -5 demonstrates a clear example of zero rate of change due to its vertical orientation on the coordinate plane.