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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 variation2
Direct Variation
  • When one thing gets larger, the other gets larger.
direct variation3
Direct Variation
  • When one thing gets larger, the other gets larger.
  • For Example:
direct variation4
Direct Variation
  • When one thing gets larger, the other gets larger.
  • For Example:
    • The more food Ando eats, the more weight he gains.
direct variation5
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.
direct variation6
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:
direct variation7
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.
direct variation8
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.
direct variation9
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.
direct variation10
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”.
direct variation11
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
direct variation12
Direct Variation
  • Write a direct variation equation for the following:
direct variation13
Direct Variation
  • Write a direct variation equation for the following:
    • The cost of postage has a constant price of 30 cents per ounce.
direct variation14
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.
direct variation15
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.
direct variation16
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?
direct variation17
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?
direct variation18
Direct Variation:
  • What sort of standard equation rule can you make for direct variations?
direct variation19
Direct Variation:
  • Manipulating equations:
direct variation20
Direct Variation:
  • Manipulating equations:
    • Show me two other ways to write the equation

y = kx

direct variation21
Direct Variation
  • Using the information given:
direct variation22
Direct Variation
  • Using the information given:
    • Write a direct variation equation that includes the given point:
direct variation23
Direct Variation
  • Using the information given:
    • Write a direct variation equation that includes the given point:
    • (1,5)
direct variation24
Direct Variation
  • Using the information given:
    • Write a direct variation equation that includes the given point:
    • (1,5)
    • The general equation is y = kx
direct variation25
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:
direct variation26
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)
direct variation27
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.
direct variation28
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
direct variation29
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
direct variation30
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
direct variation31
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
direct variation32
Direct Variation
  • How else could we have solved for k?
direct variation33
Direct Variation
  • How else could we have solved for k?
  • Write an equation of direct variation that includes the given point:
direct variation34
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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