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Direct Variation

Learn about direct variation and the constant of variation, also known as the constant of proportionality. Discover how to determine direct variation from equations, tables, and graphs.

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Direct Variation

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  1. Direct Variation Section 1.9

  2. Notes: Direct Variation • When two variable quantities have a constant ratio, their relationship is called a ________________. • The constant ratio is called the _____________________. • The constant of variation is also known as the _____________________.

  3. What is a Direct Variation? • A special equation in the form: y = kx • k is called the “constant of variation”; it is also the slope of the equation • The variables have a direct relationship; as one increases/decreases, so does the other • The graph of a direct variation always passes through the origin • Example: y = 3x

  4. Determining a Direct Variation FROM EQUATIONS: • Put equation into form (y = ) and determine if it fits the pattern y = kx Are these direct variations? y = x y = 2x – 1 3x = 5y

  5. Notes: Determine a Direct Variation • Not all situations with a constant rate of change are proportional relationships. • Likewise, not all linear functions are direct variations.

  6. Determining a Direct Variation FROM TABLES: • Solve each ordered pair for k (k = y/x) • If k is constant for each ordered pair, you have a direct variation

  7. Examples

  8. Graphing Direct Variations • Always know 1 point on the line: (0,0) • Use k (the slope) to get additional points

  9. Examples: Determine whether each linear relationship is a direct variation. If so, state the constant of proportionality 1.

  10. Essential Question • How can you determine if a linear relationship is a direct variation from an equation? A table? A graph? • __________________________________________________________________________________________________________________________________________________________________________

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