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Direct Variations

This overview discusses direct variation, a mathematical concept where two variables maintain a constant ratio. The equation y = kx (where k is the constant ratio) encapsulates this relationship. Identification methods are outlined, including graphical analysis where a line through (0,0) indicates direct variation, and tabular methods to assess proportionality in ratios. Examples, such as y = 3x, illustrate how to determine if linear functions signify direct variation and how to identify their constants of variation.

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Direct Variations

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  1. Direct Variations

  2. Vocabulary • Direct Variation • When two variables form a constant ratio • Equation: y = kx (where k is the constant ratio) • Constant of variation • The ratio k = y/x (note similarity to slope ratio)

  3. Direct Variation Identification • From a graph • If the graph crosses the y-axis at (0,0), then the relationship is a direct variation • If the graph crosses the y-axis at any other point, then the relationship is NOT a direct variation

  4. Direct Variation Graphs

  5. Direct Variation Graphs y = 3x – 1 y = 3x

  6. Direct Variation Identification • From a table • If the ratios, y/x, in the table are proportional, then the relationship is a direct variation • If even one of the ratios, y/x, in the table is NOT proportional, then the relationship is NOT a direct variation

  7. Direct Variation Tables Determine whether each linear function is a direct variation. If so, state the constant of variation.

  8. Direct Variation Tables Determine whether each linear function is a direct variation. If so, state the constant of variation.

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