Variation Chapter 9.1

Direct Variation As x increases/decreases, y increases/decreases too. y = kx k is called the Constant of Variation k ≠ 0 “y varies direct with x” or “y varies directly as x”

Inverse Variation x and y vary inversely if xy = k or k is still called the Constant of Variation and k ≠ 0 “y varies inversely with x” or “y varies inversely as x”

Joint Variation Occurs when a quantity varies directly with two or more other quantities. z = kxy Again, k is the Constant of Variation and k ≠ 0 “z varies jointly with x and y”

Summary Of Variation Direct Variationy = kx Inverse Variation Joint Variation z = kxy ***k is the Constant of Variation

Determining Variation Tell whether x and y show direct variation, inverse variation, or neither… 1.Solve for y 2.See if it matches one of the formulas: y = kx or No match means “Neither”

Determining Variation Tell Whether the following is direct variation, inverse variation or neither

Determining Variation Tell Whether the following is direct variation, inverse variation or neither

Determining Variation Tell Whether the following is direct variation, inverse variation or neither

Using Variation to Find Values Given the Type of Variation and Values for x & y 1.Write the variation formula 2.Substitute the given values 3.Solve for k 4.Use the k you found to write a specific formula 5.Use this formula and given condition to solve for missing variable.