The vertical change is called the rise.
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the slope
Slope.
Because slope is defined as change in y over change in x, for a vertical line your change in x is zero. Dividing by zero gives an undefined answer.
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
Slope is the change in y (vertical dimension) with the change in x (horizontal dimension). On a Cartesian coordinate system, the slope is equal to infinity for change in x = 0, or a vertical line.