## Combined 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 increases as well. When the value of y decreases, the value of x decreases as well. When the value of y is zero, the value of x must be zero as well.

It can also be said that y is directly proportional to x.
This relationship can be written as the mathematical equation:

y = kx,

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 decreases. When the value of y decreases, the value of x 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
If it is given that y varies jointly as x and z, it is assumed that y varies directly as x and z and the relationship can be written as:
y = kxz,
where k is the constant of proportionality.
It can also be said that y is directly proportional to x and z.

If y varies inversely as x and z, then the relationship can be written as:
y = k/(xz),
where k is the constant of proportionality.
It can also be said that y is inverse proportional to x and z.

If y varies directly as x and varies inversely as z, then the relationship can be written as:
y = kx/z,
where k is the constant of proportionality.
It can also be said that y is directly proportional to x and inversely proportional to z.

Watch the video for examples.

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