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the slope
Slope.
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.
The slope of a vertical line is not defined.
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.