Inverse Variation

The inverse variation is the product of two variables equals to a constant and the product is not equal to zero. Inverse variation is in the form of y =k/x. xy = k. Inverse variation in which value of one variable increases while the value of the other variable decreases in value is known as an inverse variation. For example think a trip of 240 miles. Rate(mph)=>20,30,40,60,80,120 and time(h)=>12,8,6,4,3,2.The numbers can be explained. As the rate of speed increase, the numbers of hour require decrease. As the rate of speed decrease, the number of hour requires increase. contrasting in a direct variation, the ratio in each data is not equivalent. The product of the value in each is equal.

Listed below is one example on Inverse Variation:

Example: If A varies inversely as B and A=2 when B=10,find A when B=4.

Solution:
Given, A=2,B=10 and A∝1/B or,A=k.1/B where k= constant of variation.
So,2=k.1/10 or k=20.

Now again,

A=k.1/B or,A=20.1/4

or,A=5.

Inverse Variation Relationship:

A inverse variation relationship in which one variable increases in value while the other decreases in value is known as an inverse variation relationship.

Consider a trip of 240 miles. The table is the time required for the trip based on the rate of travel.

Listed below is one example on Inverse Variation Relationship:

Example: If y is inversely proportional to x and y = 15 when x = 5. Find the value of y, when x = 25?

Solution:

Let, k = x/y

Plug x = 5 and y = 15 in the above equation

k = 15/5

k = 3

Now the equation becomes 3 = x/y

Now, plug x = 25

3 = y/25

3 * 25 = y

So, y = 75 when x = 25