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:
- 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.
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!