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Although all lines have the relationship that defines slope, one can argue that not all lines do have one. The exception would be vertical lines. Slope is defined as the vertical rate of change divided by the horizontal rate of change. In the case of a vertical line, there is no horizontal rate of change, and calculating slope would cause division by zero.

The closest you could come to expressing the slope of a vertical line would be ∞

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Q: Do all lines have a slope?
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