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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.
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How do you find a slope in a line?
the slope of a line = the Change in Y divided by the Change in X
How is the steepness of the line is related to the rate of change?
the steepness of the line is the slope of the line which is the rate of change; the steeper the slope, the faster the rate of change
Why can't a vertical line be used to represent rate of 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
What does the slope of a line tell you on a graph?
the rate of change on the line.
The ratio of a line's vertical change to its horizontal change?
the slope
