I assume you are asking about using differentiation. In this case, where dy-by-dx=0, there is a stationary point on the graph i.e. where the gradient is equal to 0.
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with y=mx+b dy/dx=m d^2.y/dx^2=0 The rate of change is 0
The instantaneous rate change of the variable y with respect to x must be the slope of the line at the point represented by that instant. However, the rate of change of x, with respect to y will be different [it will be the x/y slope, not the y/x slope]. It will be the reciprocal of the slope of the line. Also, if you have a time-distance graph the slope is the rate of chage of distance, ie speed. But, there is also the rate of change of speed - the acceleration - which is not DIRECTLY related to the slope. It is the rate at which the slope changes! So the answer, in normal circumstances, is no: they are the same. But you can define situations where they can be different.
0. Differentiation of a constant gives f'(x)=0.
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