As a simple example, consider the variable c which is the number of cars in a parking lot, and the variable t which is the number of tires in the parking lot. Assuming each car has four tires, we might see numbers like this.

c (number of cars) | t (number of tires) |
---|---|

0 | 0 |

1 | 4 |

2 | 8 |

3 | 12 |

4 | 16 |

These two columns stand in a very particular relationship to each other which is referred to as *direct variation*.

**Definition of “Direct Variation”**

Two variables are in “direct variation” with each other if the following relationship holds: whenever one variable doubles, the other variable doubles. Whenever one variable triples, the other variable triples. And so on.

When the left-hand column goes up, the right-hand column goes up. This is characteristic of direct variation, but it does not *prove* a direct variation. The function

The equation for this particular function is, of course,
*constant of variation*.

Note that, in real life, these relationships are not always exact! For instance, suppose *weight* of all the men in the room. The data might appear something like this:

m (number of men) | w (total weight of men, in pounds) |
---|---|

0 | 0 |

1 | 160 |

2 | 330 |

3 | 475 |

4 | 655 |

Not all men weigh the same. So this is not *exactly* a direct variation. However, looking at these numbers, you would have a very good reason to suspect that the relationship is more or less direct variation.

How can you confirm this? Recall that if this is direct variation, then it follows the equation
*approximately* the same in each case. (Try it!) So this is a good *candidate* for direct variation.

Comments:"DAISY and BRF versions of this collection are available."