Suppose that y is directly proportional to x and that y = 16 when x = 8. Find the constant of proportionality k. Then, find y when x = 12.

 24

Step-by-step explanation:

Variation: y  ∞  x

y  =  kx , where k is the constant of proportionality

now to find k, we substitute for y and x in the equation above

16 = 8k

therefore,

k = ¹⁶/₈

  = 2.

Now, to find y , we move back to the equation above and substitute for x and k to get y

y =   12(2)

  =  24

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.