Inverse & Joint Variation

1. Inverse & Joint Variation Whatyou should learn: Goal 1 Write and use inverse variation models. Goal 2 Write and use Joint variation models. 9.1 Inverse $ Joint Variation

2. Just a reminder … Direct Variation Use y = kx Means “yvaries directly with x.” k is called the constant of variation. 9.1 Inverse $ Joint Variation

3. Inverse Variation “y varies inversely with x.” k is the constant of variation. 9.1 Inverse $ Joint Variation

4. 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 9.1 Inverse $ Joint Variation

5. 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 9.1 Inverse $ Joint Variation

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. 9.1 Inverse $ Joint Variation

7. Part 1:The variable z varies Jointly withx & y. Use the given values to write an equation relation x, y, and z. Part 2: Then find z wheny = 7andx = -4. for Part 2: Find z. for Part 1:Find k. Given values: x = -12, y = 4, z = 2 9.1 Inverse $ Joint Variation

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. 9.1 Inverse $ Joint Variation

9. Assignment 9.1 Inverse $ Joint Variation