Elsie

**Solution- **Direct variation is defined as two variables which increase or decrease at a constant rate. This constant rate is denoted by *k. *

The equation for direct variation can be written as,

Where x and y are two variables and k is a constant.

Some examples of direct variation in real life are,

- A motor vehicle with a speed ‘x’ covers distance ‘y’ in an hour. In this case, if the speed is increased, distance covered will be more in the same amount of time.
- If a constant ‘p’ is multiplied by numbers in increasing order, the resultant will be in increasing order.
- A device which needs to be charged for ‘x’ hours to run for time ‘y’, in order to increase its running hours will have to be charged for more time.

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**Similar Problems**

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**Question- How do you find the direct variation equation if y varies directly as x when , ?**

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**Solution-**

From the information provided in the problem,

The equation for direct variation is given as,

Therefore,

On substituting the given values we get

Therefore the equation of direct variation will be represented as,

Thus, the direct variation equation, if y varies directly as x, will be given as .

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**Question-What are some examples of inverse variation?**

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Examples of such variation are,

- A motor vehicle with a speed ‘x’ covers a particular distance in time ‘y’. In this case, if the speed is increased, the equal distance will be covered in lesser time.
- If a constant number ‘x’ is divided by increasing values of numbers, the resultant values will be in decreasing order.
- If a work requires 20 individual and gets completed in 10 days, the increase in manpower will lead to a decrease in time required.

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