Direct and inverse proportion

Direct and inverse proportion 

Direct Proportion:
In direct proportion, two quantities vary in such a way that an increase in one quantity leads to a proportionate increase in the other quantity, or a decrease in one quantity leads to a proportionate decrease in the other quantity. Mathematically,

 if two variables x and y are in direct proportion, it can be represented as

 x ∝ y or x = ky,

 where k is the constant of proportionality.

Example:

 The time taken to complete a journey is directly proportional to the distance traveled. If it takes 2 hours to travel a distance of 100 kilometers, then it would take 4 hours to travel a distance of 200 kilometers. Here, time (x) and distance (y) are in direct proportion.

Inverse Proportion:
In inverse proportion, two quantities vary in such a way that an increase in one quantity leads to a proportionate decrease in the other quantity, or a decrease in one quantity leads to a proportionate increase in the other quantity. Mathematically,

 if two variables x and y are in inverse proportion, it can be represented as

 x ∝ 1/y or xy = k,

 where k is the constant of proportionality.

Example: 

The speed of a car and the time taken to travel a fixed distance are inversely proportional. If a car travels a distance of 100 kilometers at a speed of 50 kilometers per hour, then it would take 2 hours. However, if the car travels at a speed of 100 kilometers per hour, then it would take only 1 hour to cover the same distance. Here, speed (x) and time (y) are in inverse proportion.

In both direct and inverse proportion, the constant of proportionality (k) remains the same throughout the relationship between the two variables