Find an equation of combined variation where a varies directly as b and inversely as c. One set of values is a = 4, b = 12, and c = 9. Find a when b = 7 and c = 3.

Combined equation is  

Step-by-step explanation:

a varies directly as b and  inversely as c.

This can be written as

a =

a =  kb

where k is the proportionality constant

-------------------------------------(1)

Now lets find the k value bu substituting the given a, b,c values

36 =  12 k

k = 3

Thus the eq(1) becomes

Let us now find the value of a  when b=7  and c = 3

a = 7

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)