## Variation

Variation explains how the change in one or more variables affects another variable. In essence, in tells us the relationship between two or more variables. There are two types of variation discussed in this post, as well as a combination of the two types of variations.

Variation is synonymous to proportionality. The terms “directly proportional” and “varies directly as” can be used interchangeably as can the terms “inversely proportional” and “varies inversely as”.

## Direct variation

The first type of variation is direct variation. If a variable, y **varies directly as** another variable x, when the value of y * increases*, the value of x

*as well. When the value of y*

**increases***, the value of x*

**decreases***as well. When the value of y is zero, the value of x must be zero as well.*

**decreases**It can also be said that y is **directly proportional** to x.

This relationship can be written as the mathematical equation:

y = *k*x,

where *k* is the constant of proportionality.

Try out the questions in the video before I show you the workings to each one.

*Watch the video for a detailed explanation and examples.*

## Inverse variation

If a variable, y **varies inversely as** another variable x, when the value of y * increases*, the value of x

*. When the value of y*

**decreases***, the value of x*

**decreases***.*

**increases**It can also be said that y is **inversely proportional** to x.

This relationship can be written as the mathematical equation:

y = *k/*x,

where *k* is the constant of proportionality.

Try out the questions in the video before I show you the workings to each one.

*Watch the video for a detailed explanation and examples.*

## Combined variation

The two variations learnt earlier in this post can be combined in one of three ways:

- combined direct variations
- combined inverse variations
- combined direct and inverse variations

**varies jointly**as x and z, it is assumed that y

**varies directly**as x and z and the relationship can be written as:

*k*xz,

*k*is the constant of proportionality.

**directly proportional**to x and z.

**varies inversely**as x and z, then the relationship can be written as:

*k*/(xz),

*k*is the constant of proportionality.

**inverse proportional**to x and z.

**varies directly**as x and

**varies inversely**as z, then the relationship can be written as:

*k*x/z,

*k*is the constant of proportionality.

**directly proportional**to x and

**inversely proportional**to z.

*Watch the video for examples.*

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