When *y* varies **directly** as both *x* and *w*, we say that *y* varies **jointly** as *x* and *w*. When you first looked at *direct variation*, you focused mainly on a single *dependent* and *independent* variable (i.e. *y* and *x*, respectively). This time the equation directly depends one 2 or more independent variables (*x* and *w)*. The three variables introduced above are related by the following equation:

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- Where, as before,
*k*is a**constant of proportionality**

The video below shows two examples of joint variation.

Distinguishing between *joint* and **combined variation** is sometimes confusing for students. Just like joint variation, *combined variation* relates two or more independent variable to the dependent variable. However, as the name implies, the variables don’t have to be directly proportional. Rather, you can combine direct, inverse, and jointly related variables. Just as before, the way they are related can be found by careful reading of the problem statement.

**Question****2**and**Question 3**can be accessed by clicking the links.

The last video in this lesson shows two more examples of joint and combined variation. *Can you tell which of the two questions featured is joint and which is combined?* Write a comment below!