1. 9.1 Inverse & Joint Variation

2. Objectives/Assignment
Write and use inverse variation models
Write and us joint variation models
Assignment: 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. 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

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.