Direct Variation

If two quantities are linked in such a way that an increase in one quantity leads to a corresponding increase in the other and vice-versa,then such a variation is called a direct variation. If two quantities are in direct variation ,then we also say that they are proportional to each other .

Illustration: If the cost of 93 m of a certain kind of plastic sheet Rs 1395, then what would it cost to buy 105 m of such plastic sheet?

Solution: Let the cost of plastic sheet 105m is x

According to Direct Variation:

On solving as these numbers we see that 1395 is divisible by 93.

x = 1575 Rs

Illustration: In which of the following tables,a and b vary directly. Also ,find the constant of variation if a and b are in direct variation .

(i)

(ii)

(iii)

Solution:

(i) We have,

Thus, the ratio of the corresponding values of a and b is constant

. 

Hence, a and b are in direct variation with the constant of variation equal to 1/3

(ii) We have, 

.  

This shows that the ratio of the corresponding values of a and b is constant and is equal to .Thus, a and b vary directly. The constant of variation is

(iii) It is evident from the table that the ratio of the corresponding values of a and b is not constant. So, a and b are not in direct variation i.e they do not vary directly .