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Direct Variation  Inverse Variation 

8.1 Model Inverse and Joint Variation. By the end of the lesson you should: classify direct and inverse variations write an inverse variation equation Write and inverse variation model write a joint variation equation compare variations. Direct Variation  Inverse Variation .

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Direct Variation  Inverse Variation 

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  1. 8.1 Model Inverse and Joint Variation • By the end of the lesson you should: • classify direct and inverse variations • write an inverse variation equation • Write and inverse variation model • write a joint variation equation • compare variations Direct Variation  Inverse Variation  CLASSIFICATION: (direct, inverse, or neither)

  2. WRITE AN INVERSE VARIATION EQUATION • The variables x and y vary inversely, and y = 7 when x = 4. Write an • equation that relates x and y. Then find y when x = 2. • step 1: write the general equation that relates x and y inversely. • step 2: plug in x = _____and y = _____ • step 3: solve for a • step 4: plug a into the inverse equation. • step 5: evaluate that equation when x = _____

  3. YOUR TURN: 1. The variables x and y vary inversely, and y = -1 when x = 8. Write an equation that relates x and y. Then find y when x = 2. 2. The variables x and y vary inversely, and y = 15 when x = (1/3). Write an equation that relates x and y. Then find y when x = -10.

  4. JOINT VARIATION ...is a direct variation with the product of 2 or more other quantities z = axy or p = aqrs Example: The variable z varies jointly with x and y. Also, z = -75 when x = 3 and y = -5. Write an equation that relates x, y, and z. Then find z when x = 2 and y = 6. step 1: write the general equation that relates x, y, and z jointly. step 2: plug in z = ______ x = ___ _ y = ___ _ and solve for a step 3: plug a into the joint variation equation. step 4: solve for z when x = and y = _____

  5. YOUR TURN: 1. The variable z varies jointly with x and y. Also, z = 60 when x = -4 and y = 5. Write an equation that relates x, y, and z. Then find z when x = 7 and y = 2. 2. The variable z varies jointly with x and y. Also, z = 24 when x = 4 and y = -3. Write an equation that relates x, y, and z. Then find z when x = -2 and y = 5.

  6. WRITE DIFFERENT TYPES OF VARIATIONS • RELATIONSHIP EQUATION • 1. y varies inversely with x • 2. z varies jointly with x, y, and r • 3. y varies inversely with the square of x • 4. z varies directly with y and inversely with x • 5. x varies jointly with t and r and inversely with s • q varies inversely with the square of y • and jointly with x and z

  7. WELCOME TO REAL LIFE: The number of songs that can be stored on an iPod varies inversely with the average size of a song. A certain iPod can store 2500 songs when the average size of a song is 4 megabytes (MB). ....use the equation to write a relationship between the number of songs "n" that will fit on the iPod and the average song size "s." ....then describe what you think will happen to the number of songs as the average song size increases. ....lets say the average size of the songs are 2 MB, 2.5 MB, 3 MB, 5 MB

  8. Assignment: Pp. 555-556 (3-6)(13-19odd) (25-29odd)(31-33, 37)

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