# Variation

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A series of free, online Intermediate Algebra Lessons or Algebra II lessons.

Videos, worksheets, and activities to help Algebra students.

In this lesson, we will learn

- direct variation
- how to solve direct variation word problems
- direct variation equations
- indirect or inverse variation
- how to solve indirect or inverse variation word problems
- joint and combined variation
- how to solve joint and combined variation word problems

### Direct Variation

We often use the term direct variation to describe a form of dependence of one variable on another. An equation that makes a line and crosses the origin is a form of direct variation, where the magnitude of x increases or decreases directly as y increases or decreases. Direct variation and inverse variation are used often in science when modeling activity, such as speed or velocity.

This video explains direct variation and solves application problems.

Direct Variation Applications

### Direct Variation Equation

This video provides and example of how to determine a direct variation equation from given information and then determine y with a given value of x.

This video explains how to graph a linear direct variation equation with a positive slope. The equation is in the form y = mx + b with b = 0.

This video explains how to graph a linear direct variation equation with a negative slope. The equation is in the form y = mx + b with b = 0.

### Indirect or Inverse Variation

When modeling real world situations, we often use what's called inverse or indirect variation to describe a relation between two variables. Indirect variation is a relation in which the absolute value of one variable gets smaller while the other gets larger. Indirect variation and direct variation are important concepts to understand when learning equations and interpreting graphs.

This video explains and provides examples of inverse variation.

This video provides an example of how to solve a basic inverse variation problem

This video provides an example of how to solve a basic inverse variation problem not using x and y.

This video provides an example of how to solve a inverse variation problem when k is a fraction.

This video provides an inverse variation example relating the number of workers to the number of hours it takes to complete a job.

This video provides an inverse variation example relating the loudness in decibels and the distance from a sound source.

### Joint and Combined Variation

In Algebra, sometimes we have functions that vary in more than one element. When this happens, we say that the functions have joint variation or combined variation. Joint variation is direct variation to more than one variable (for example, d = (r)(t)). With combined variation, we have both direct variation and indirect variation

How to define joint and combined variation.

Solve using Joint Variation

Solving a Joint Variation Problem involving Volume

How to set up combined variation problems.

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