## Did you know?

We also have Bitesize study guides covering many subjects at National 4 and National 5 on our Knowledge & Learning BETA website.

Home > Maths I > Relationships > Direct variation

Maths I

Direct variation

Back

# Finding the variation formula

Variation is another word for proportion. If two quantities and are in proportion to one another, we say that varies directly as and write:

## Example

Let stand for the amount in pence you pay for bananas. Let be the number of bananas you buy.

Study the table.

Number of bananas (B)123456
Amount or cost (A)20406080100120

Notice that if you double the number of bananas you buy, you double the amount you have to pay. Or if you multiply the number of bananas by , the amount you pay is also multiplied by . And so on.

So varies directly as -

We can now write this as , where is the constant of variation.

Choose any pair of values from the table above, say and .

Put these values into and we get -

or

Therefore, i.e. the constant of variation is .

We can now write and this is called the variation formula.

The graph of against is shown below.

Notice that the graph is a straight line through the origin.

Back

BBC iD