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Learn about inverse and joint variation in mathematics, explore equations, constants, and relationships between variables. Practice solving problems to determine direct, inverse, or joint variation. Enhance your mathematical skills with practical examples.
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Just a reminder from chapter 2 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.
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.
