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9.1 Inverse & Joint Variation

9.1 Inverse & Joint Variation. Objectives/Assignment. Write and use inverse variation models Write and us joint variation models Assignment: 21-47 odd. Just a reminder from chapter 2. Direct Variation Use y=kx. Means “y varies directly with x.” k is called the constant of variation.

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9.1 Inverse & Joint Variation

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  1. 9.1 Inverse & Joint Variation

  2. Objectives/Assignment Write and use inverse variation models Write and us joint variation models Assignment: 21-47 odd

  3. Just a reminder from chapter 2 Direct Variation Use y=kx. Means “y varies directly with x.” k is called the constant of variation.

  4. New stuff! Inverse Variation “y varies inversely with x.” k is the constant of variation.

  5. Ex: tell whether x & y show direct variation, inverse variation, or neither. • xy=4.8 • y=x+4 Inverse Variation Hint: Solve the equation for y and take notice of the relationship. Neither Direct Variation

  6. Ex: The variables x & y vary inversely, and y=8 when x=3. • Write an equation that relates x & y. k=24 • Find y when x= -4. y= -6

  7. Joint Variation • When a quantity varies directly as the product of 2 or more other quantities. • For example: if z varies jointly with x & y, then z=kxy. • Ex: if y varies inversely with the square of x, then y=k/x2. • Ex: if z varies directly with y and inversely with x, then z=ky/x.

  8. Examples: Write an equation. • y varies directly with x and inversely with z2. • y varies inversely with x3. • y varies directly with x2 and inversely with z. • z varies jointly with x2 and y. • y varies inversely with x and z.

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