Question

Suppose x varies directly as y and inversely as z. When y=2 and z=3, x=7. When y=6 and z=7, x=?

Answer 1

x varies directly means y :

\[x \; \; \alpha \; \; y\]

Answer 2

x=9 ??

Answer 3

So just put a proportionality constant there, let us say k:

\[x = ky\]

Answer 4

\[\huge x=\frac{ ky }{ z }\]

Answer 5

k is any constant

Answer 6

directly means over, inversely means times.

if you graphed a function that had three variables:


would be two representations