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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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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
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
What does a slope of a line tell you?
The rate of change
What is the rate of change of a line called?
slope
What does the slope of a line tell you on a graph?
the rate of change on the line.
