Direct Variation

Question

Find an equation of variation in which y varies directly as the square of x and y = 6 when x = 3.

Answer 1

Kate, we have that y/x² and want to find a value for k in y = kx².  If we plug in what we have, we get 6 = 9k, so k = 2/3, so our equation is y = (2/3)x.

Answer 2

Kate:

 

You can set your problem up like this:

 

y = C·x², where "C" is an unknown proportionality constant. Now substitute y = 6 and x = 3 to solve for C and you will have your equation!