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Joint or Combined Variation

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More Lessons for Grade 9

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Videos, worksheets, games and activities to help Algebra students learn about joint or combined variation.

What is Joint Variation or Combined Variation?
Joint Variation or Combined Variation is when one quantity varies directly as the product of at least two other quantities.

Joint Variation

Joint Variation
Suppose y varies jointly as x and z. What is y when x = 2 and y = 3, if y = 20 when x = 4 and y = 3?

Joint Variation

Joint Variation Application
The energy that an item possesses due to its motion is called kinetic energy. The kinetic energy of an object (which is measured in joules) varies jointly with the mass of the object and the square of its velocity.
If the kinetic energy of a 3 kg ball traveling 12 m/s is 216 Joules, how is the mass of a ball that generates 250 Joules of energy when traveling at 10 m/s?
Direct, Inverse and Joint Variation
Determine whether the data in the table is an example of direct, inverse or joint variation. Then, identify the equation that represents the relationship.


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 set up and solve combined variation problems.
Lesson on combining direct and inverse or joint and inverse variation

How to solve problems involving joint and combined variation
y varies jointly as x and z and inversely as w, and y = 3/2, when x = 2, z =3 and w = 4. Find the equation of variation.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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