I need help on this 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.

Option 1: $30 an hour plus a nonrefundable deposit of $50 option 2: $20 an hour plus a nonrefundable deposit of $75 kyle is renting a jetski for the day. if he can rent the jetski in one hour increments, what is the minimum number of hours must he rent the jetski for option 2 to be a better deal then option 1?

What is the smallest integer n such that n\sqrt{2} is greater than 20