# Algebra I: Variation

### Introduction and Summary

This chapter deals with two specific types of relationships between variables -- direct variation and inverse variation.

When two variables vary directly, one increases when the other increases and decreases when the other decreases. They always increase or decrease by the same magnitude as each other. The first section in this chapter deals with this relationship. It explains how to write an equation to describe it and how to find the value of one variable, given any value of the other.

When two variables vary inversely, one increases when the other decreases, and vice versa. One variable increases by the same magnitude that the other decreases. The second section deals with inverse variation. As in the previous section, the reader will learn how to write an equation to describe this variation and how to determine the value of one variable, given the value of the other.

Many variables that we encounter in everyday life vary directly or inversely as each other. For example, the time it takes to travel from one place to another varies directly with the distance and varies inversely with the average speed. The material in this chapter will aide in understanding of these everyday variations, and will explain how to determine the value of one quantity, given the value of another (we can determine total time needed to travel a given distance, for instance).

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