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Mastering Direct Variation: Formulas, Graphs & Word Problems

Learn about direct variation equations, constant of variation, graphing methods, and solving word problems. Understand how variables relate and work through examples to grasp the concepts effectively.

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Mastering Direct Variation: Formulas, Graphs & Word Problems

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  1. Direct Variation 5-2

  2. 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

  3. 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

  4. 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

  5. Examples

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

  7. Examples Graph: y = -3x Graph:

  8. Writing Direct Variation Equations • Substitute variables into direct variation equation, y = kx • Solve for k • Write the direct variation equation with k

  9. Examples Write a direct variation eq’n for x = 4 and y = 12. Write a direct variation eq’n for x = -9 and y = 3.

  10. Direct Variation Word Problems • Determine which value is x and which is y • Remember y varies directly with x • Substitute information into direct variation equation • Solve for k • Rewrite equation with k • If needed, substitute remaining information to solve for the required variable

  11. Example Mary’s salary varies directly with the number of hours she works. If Mary’s salary is $273 when she works 28 hours, write a direct variation equation relating these variables. How many hours would she have to work to earn $351?

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