1. Inverse & Joint Variation
What you 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 “y varies directly with x.”
k is called the constant of variation.
9.1 Inverse $ Joint Variation

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

4. 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
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 with x & y
Part 1: The variable z varies Jointly with x & y. Use the given values to write an equation relation x, y, and z. Part 2: Then find z when y = 7 and x = -4.
for Part 1: Find k.
for Part 2: Find z.
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