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5.2 Direct Variation

5.2 Direct Variation. D irect Variation: the relationship that can be represented by a function if the form:. y = k x. Constant of variation: the constant variable K is the coefficient of x on the y= kx equation.

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5.2 Direct Variation

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  1. 5.2 Direct Variation Direct Variation: the relationship that can be represented by a function if the form: y = kx Constant of variation: the constant variable K is the coefficient of x on the y=kx equation. Inverse variation: the relationship that can be represented by the function: y = Joint Variation: the relationship that can be represented by the function: y = kxz

  2. Real World:

  3. Identifying a Direct Variation:If the equation can be written in y = kx we have a direct variation. • Ex: • Does the equation represent a direct variation? • a) 7y = 2x b) 3y + 4x = 8

  4. Ex: (solution)If we can writer the equation in y = kx we have a direct variation. a) 7y = 2x Inverse of Multiplication ___ __ 7 7 Equation is in y=kx with k= y = x Isolate y, subtract 4x and divide by 3 b) 3y + 4x = 8 y = x+ Equation is not in y=kx

  5. WRITING DIRECT VARIATION EQUATIONS: To write a direct variation equation we must first find the constant of variation k using ordered pairs given. Ex: Suppose y varies directly with x, and y = 35 when x = 5. What direct variation equation relates x and y? What is the value of y when x = 9?

  6. AGAIN: To write a direct variation equation we must first find the constant of variation k using ordered pairs given. From the problem, we are given the following: y = 35 when x = 5. That is: (5, 35) Since we have “varies directly” we must have an equation on the form: y = kx Using the equation and info given, we have: 35 = k(5) k = 35/5 = 7

  7. Once we know the constant of variation(K = 7) we can now write the direct variation equation as follows: y = kx y = 7x We now go further and find the value of y when x = 9 as follows: y = 7x y = 7(9) Thus: y = 63 when x = 9.

  8. YOU TRY IT: Suppose y varies directly with x, and y = 10 when x = -2. Write a direct variation equation and find the value of y when x = - 15.

  9. YOU TRY IT (SOLUTION): Given: y = 10, x = - 2 Varies Directly equation: y = kx To find the constant of variation (k): y = kx 10 = k(-2) K = - 5 Therefore our equation is: y = -5x Using this equation to find y when x = -15 y = -5x y = -5(-15)  y = 75.

  10. Real World: Let’s solve it

  11. Real World: Let’s solve it Using the direct variation equation and y = 2mi when x = 10s y = kx 2 = k(10) k = = Thus the direct variation eq: y = x

  12. GRAPHING DIRECT VARIATIONS: To graph a direct variation equation we must go back to tables: Remember: the Independent variable(x) is chosen by you if you are not given any x values.

  13. Ex: Graph f(x) = -7x Now we must graph the ordered pairs (last column)

  14. Y = -7x

  15. YOU TRY IT: Graph y = 2X

  16. YOU TRY IT: (SOLUTION) Graph y = 2x

  17. Y = 2x

  18. VIDEOS: Graphs https://www.khanacademy.org/math/algebra/algebra-functions/direct_inverse_variation/v/direct-and-inverse-variation https://www.khanacademy.org/math/algebra/algebra-functions/direct_inverse_variation/v/recognizing-direct-and-inverse-variation

  19. Class Work: Pages: 302-303 Problems: As many as needed to master the concept

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