9.1 Inverse & Joint Variation

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Presentation transcript:

9.1 Inverse & Joint Variation

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

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

Identifying inverse vs. direct Direct Variation= as x increases, y increases Inverse Variation= as x increases, y decreases Neither is always an option too

Hint: Solve the equation for y and take notice of the relationship. 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

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/x2. 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 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.

Assignment Pg. 491(6, 8, 10, 12, 14, 20, 26, 28, 34,36)