8.1.1 Variation Functions
Key Objectives • Solve problems involving direct, inverse, joint, and combined variation. • Write, graph, and evaluate variation functions. Key Terms • A direct variation is a linear relationship of the form y = kx , where k ≠ 0. The ratio of the two quantities x and y is constant. • The constant of variation is the constant k in a variation equation. • A joint variation is a relationship among three variables that can be written in the form y = kxz , where k ≠ 0. • An inverse variation is a relationship of the form y = k / x , where k ≠ 0 and x ≠ 0. The product of the two quantities x and y is constant. • Combined variation is a relationship containing both direct and inverse variation. Example 1 Writing and Graphing Direct Variation If y varies directly as x , then the relationship between x and y , called a direct variation, can be described by an equation of the form y = kx , where k ≠ 0. In this relationship, k is the constant of variation. The graph of a direct variation is a line with slope k that passes through the origin.
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