9.1 Inverse & Joint Variation p.534 What is direct variation? What is inverse variation? What is joint variation?

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Presentation transcript:

9.1 Inverse & Joint Variation p.534 What is direct variation? What is inverse variation? What is joint variation?

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

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

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

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

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/x 2. Ex: if z varies directly with y and inversely with x, then z=ky/x.

Examples: Write an equation. y varies directly with x and inversely with z 2. y varies inversely with x 3. y varies directly with x 2 and inversely with z. z varies jointly with x 2 and y. y varies inversely with x and z.

What is direct variation?What is direct variation? y varies directly with x (y = kx) What is inverse variation?What is inverse variation? y varies inversely with x (y = k/x) What is joint variation?What is joint variation? A quantity varies directly as the product of two or more other quantities ( y = kxy)

Assignment p ,39-43