1. 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.

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

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

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.

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