For every cm you go along x, you change a certain amount in y cm. So y is changing a certain amount per unit change in x. If the plot were y versus t, then y would be called changing at a certain amount per second, like a velocity. Velocity is another word for rate of change of y.
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slope
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.
In mathematics, a constant rate of change is called a slope. For linear functions, the slope would describe the curve of the function. The world "constant" in this context means the slope and therefore angle of the curve will not change.
the rate of change is related to the slope; the higher the slope, the higher the rate. If the line is vertical, that is infinite slope or infinite rate of change which is not possible
The rate of change is the same as the slope.