Direct Variation

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 variables 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:


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D(km)	24	12	48	36
T(km)	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

The ratio of the corresponding values of D and T is always same. So, we can say that, the value of D/T is constant . If this constant be k, then D/T = K or, D= KT. This constant is called the Constant of Variation.

Hence, if D ∝ T then D = KT where K = Constant of Variation.
Thus, if A ∝ B then A=mB where m is the constant of variation and is independent of A and B.
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