The variable z is directly proportional to x. when x is 5, z has the value 55.

what is the value of z when x = 12

Direct variation is of the form y=kx, in this case:

z=kx, we are given the point (5,55) so we can solve for the constant of variation

55=5k  divide both sides by 5

11=k so our equation is:

z=11x, so when x=12

z=11(12)

z=132