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Assuming the variables are x (horizontal) and y (vertical), the slope of a straight line is defined as "rise over run". That is, the change in y divided by a change in x. This is exactly what the rate of change in y with respect to x, is.

If the line is a curve, the instantaneous slope is defined as the gradient of the tangent to the curve and is the limiting value (as dx tends to 0) of the same measure.

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Q: How does the slope of a line represent the rate of change?
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