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Direct Variation

Direct Variation. Direct Variation. Direct Variation. When one thing gets larger, the other gets larger. Direct Variation. When one thing gets larger, the other gets larger. For Example:. Direct Variation. When one thing gets larger, the other gets larger. For Example:

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Direct Variation

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  1. Direct Variation

  2. Direct Variation

  3. Direct Variation • When one thing gets larger, the other gets larger.

  4. Direct Variation • When one thing gets larger, the other gets larger. • For Example:

  5. Direct Variation • When one thing gets larger, the other gets larger. • For Example: • The more food Ando eats, the more weight he gains.

  6. Direct Variation • When one thing gets larger, the other gets larger. • For Example: • The more food Ando eats, the more weight he gains. • When the amount of food Ando eats goes up, the amount of weight he gains goes up.

  7. Direct Variation • When one thing gets larger, the other gets larger. • For Example: • The more food Ando eats, the more weight he gains. • When the amount of food Ando eats goes up, the amount of weight he gains goes up. • As an equation it would look like this:

  8. Direct Variation • When one thing gets larger, the other gets larger. • For Example: • The more food Ando eats, the more weight he gains. • When the amount of food Ando eats goes up, the amount of weight he gains goes up. • As an equation it would look like this: • W is Ando’s weight.

  9. Direct Variation • When one thing gets larger, the other gets larger. • For Example: • The more food Ando eats, the more weight he gains. • When the amount of food Ando eats goes up, the amount of weight he gains goes up. • As an equation it would look like this: • W is Ando’s weight. • E is the amount Ando eats.

  10. Direct Variation • When one thing gets larger, the other gets larger. • For Example: • The more food Ando eats, the more weight he gains. • When the amount of food Ando eats goes up, the amount of weight he gains goes up. • As an equation it would look like this: • W is Ando’s weight. • E is the amount Ando eats. • K is ALWAYS the constant amount that he gains.

  11. Direct Variation • When one thing gets larger, the other gets larger. • For Example: • The more food Ando eats, the more weight he gains. • When the amount of food Ando eats goes up, the amount of weight he gains goes up. • As an equation it would look like this: • W is Ando’s weight. • E is the amount Ando eats. • K is ALWAYS the constant amount that he gains. • K is called the “constant of variation”.

  12. Direct Variation • When one thing gets larger, the other gets larger. • For Example: • The more food Ando eats, the more weight he gains. • When the amount of food Ando eats goes up, the amount of weight he gains goes up. • As an equation it would look like this: • W is Ando’s weight. • E is the amount Ando eats. • K is ALWAYS the constant amount that he gains. • K is called the “constant of variation”. • W = KE

  13. Direct Variation • Write a direct variation equation for the following:

  14. Direct Variation • Write a direct variation equation for the following: • The cost of postage has a constant price of 30 cents per ounce.

  15. Direct Variation • Write a direct variation equation for the following: • The cost of postage has a constant price of 30 cents per ounce. • The distance traveled has a constant speed of 30 miles per hour.

  16. Direct Variation • Write a direct variation equation for the following: • The cost of postage has a constant price of 30 cents per ounce. • The distance traveled has a constant speed of 30 miles per hour. • The points scored has a constant amount of 6 per touchdown.

  17. Direct Variation • Write a direct variation equation for the following: • The cost of postage has a constant price of 30 cents per ounce. • The distance traveled has a constant speed of 30 miles per hour. • The points scored has a constant amount of 6 per touchdown. • What is the DEPENDENT and INDEPENDENT variable in each equation?

  18. Direct Variation • Write a direct variation equation for the following: • The cost of postage has a constant price of 30 cents per ounce. • The distance traveled has a constant speed of 30 miles per hour. • The points scored has a constant amount of 6 per touchdown. • What is the DEPENDENT and INDEPENDENT variable in each equation? • What variable represents dependent and what variable represents independent in general?

  19. Direct Variation: • What sort of standard equation rule can you make for direct variations?

  20. Direct Variation: • Manipulating equations:

  21. Direct Variation: • Manipulating equations: • Show me two other ways to write the equation y = kx

  22. Direct Variation • Using the information given:

  23. Direct Variation • Using the information given: • Write a direct variation equation that includes the given point:

  24. Direct Variation • Using the information given: • Write a direct variation equation that includes the given point: • (1,5)

  25. Direct Variation • Using the information given: • Write a direct variation equation that includes the given point: • (1,5) • The general equation is y = kx

  26. Direct Variation • Using the information given: • Write a direct variation equation that includes the given point: • (1,5) • The general equation is y = kx • Put in the information you know:

  27. Direct Variation • Using the information given: • Write a direct variation equation that includes the given point: • (1,5) • The general equation is y = kx • Put in the information you know: • 5 = k(1)

  28. Direct Variation • Using the information given: • Write a direct variation equation that includes the given point: • (1,5) • The general equation is y = kx • Put in the information you know: • 5 = k(1) • Solve for k.

  29. Direct Variation • Using the information given: • Write a direct variation equation that includes the given point: • (1,5) • The general equation is y = kx • Put in the information you know: • 5 = k(1) • Solve for k. • k(1) = 5

  30. Direct Variation • Using the information given: • Write a direct variation equation that includes the given point: • (1,5) • The general equation is y = kx • Put in the information you know: • 5 = k(1) • Solve for k. • k(1) = 5 • k = 5/1

  31. Direct Variation • Using the information given: • Write a direct variation equation that includes the given point: • (1,5) • The general equation is y = kx • Put in the information you know: • 5 = k(1) • Solve for k. • k(1) = 5 • k = 5/1 k = 5

  32. Direct Variation • Using the information given: • Write a direct variation equation that includes the given point: • (1,5) • The general equation is y = kx • Put in the information you know: • 5 = k(1) • Solve for k. • k(1) = 5 • k = 5/1 k = 5 y = 5x

  33. Direct Variation • How else could we have solved for k?

  34. Direct Variation • How else could we have solved for k? • Write an equation of direct variation that includes the given point:

  35. Direct Variation • How else could we have solved for k? • Write an equation of direct variation that includes the given point: • (6,3)

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