The steepest line possible is a vertical line. Its slope is bigger than any possible number you can think of, because it can change its height by any amount in zero time. Its slope is 'undefined', meaning that there's no number that can describe it. Some people would say it's 'infinity', but that's not a number.
The steepest line possible is a vertical line with an undefined slope. This is because a vertical line does not have a defined horizontal change; instead, it only has vertical change. A slope is undefined when it cannot be calculated due to division by zero.
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