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Direct Variation

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Direct Variation

- When one thing gets larger, the other gets larger.

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

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

- 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.

- 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:

- 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.

- 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.

- 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.

- 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”.

- 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

- Write a direct variation equation for the following:

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

- 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.

- 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.

- 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?

- 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?

- What sort of standard equation rule can you make for direct variations?

- Manipulating equations:

- Manipulating equations:
- Show me two other ways to write the equation
y = kx

- Show me two other ways to write the equation

- Using the information given:

- Using the information given:
- Write a direct variation equation that includes the given point:

- Using the information given:
- Write a direct variation equation that includes the given point:
- (1,5)

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

- 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:

- 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)

- 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.

- 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

- 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

- 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

- 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

- How else could we have solved for k?

- How else could we have solved for k?
- Write an equation of direct variation that includes the given point:

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