Somebody help please

Karianne and lucius are analyzing a linear function on a graph. karianne says that unit rate is equal to rate of change, but that slope is calculated differently. lucius says that unit rate, rate of change, and slope are calculated the same way. who is correct? explain your answer.

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*segment an is an altitude of right ? abc with a right angle at a. if ab = 2root 5 in and nc = 1 in, find bn, an, ac.