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Yes and the straight line could be parallel to the x or y axes
An undefined slope is just a line straight down. The slope is undefined.
The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.
zero is horizontal, undefined is vertical
The slope of a line is undefined if the line is vertical.