If y varies directly as x , and y is 400 when x is r and y is r when x is 4 , what is the numeric constant of variation in this relation?

For direct variation, y = kx, where k is the constant of variation. The two conditions give 400 = kr and r = 4k; substituting r = 4k into the first equation gives 400 = 4k², so k² = 100. Thus the numeric constant is 10, choice D.

AI-written and checked against the verified answer.