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There are three basic types of variation: direct variation (y=kx), inverse variation , and joint variation. The joint variation equation (z = kxy) is an example where the variable z varies jointly with the two variables x and y. All joint variation equations represent variables that vary jointly with two or more other variables. In each case, k is called the constant of variation.

More complicated variation equations can be created from these basic formats. Consider the two statements shown below and their corresponding variation equations:

 Relationship Equation y varies inversely with the square of x y varies directly with z y = kz If you put these two statements together you get the statement and corresponding variation equation: Relationship Equation y varies inversely with the squareof x and directly with z You may want to try breaking up the statements in Exercises 45-47 into two separate statements and determine their corresponding equations. Then you can create one single variation equation from the two separate variation equations much like was done in the example above.