What is a Direct Variation

Introduction:

      The mathematical relationship between two variables, expressed in the equation in which one of the variable is equal to the constant multiple of the other of an equation or function expressing direct variation. The relationship between the two variables remains in a constant ratio. It is called as direct variation.

      If two varables A and B are so related that when A increases (or decreases) in a given ratio,B also increases(or,decreases)in the same ratio, then A is said to vary directly as B(or,A is said to vary as B).This is symbolically written as, A  ∝ B ( ' A  varies as B' ).
Suppose a train moving at a uniform speed travels D km in T minutes.
Now,consider the following table:

D(km)	24	12	48	36
T(min)	30	15	60	45

 The Table shows that T is increased or decreased in the same ratio as the distance D.Hence , the variables D and T are in Direct Variation(i.e., D∝T).
We also see that , (24 / 30)=4/5 ,   (12 / 15)=4/5 ,  (48 / 60)=4/5 ,  (36 / 45)=4/5

Hope you like the above explanation. Please leave your comments, if you have any doubts.