Write an equation in vertex form (based on the transformation)

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If given an equation of a line such as -1/2x+6 how would you create an equation of a line parallel and perpendicula to this line that goes through another point such as (4,10)

Me. i can't figure out this question. give an explanation too. .

Describe how to determine the average rate of change between x = 4 and x = 6 for the function f(x) = 2x^3 + 4. include the average rate of change in your answer.