1. 4.7 Variation

2. k is constant of variation
Direct Variation
k is constant of variation
“y varies directly as x”
“y is directly proportional to x”
As x ↑, y ↑ or As x ↓, y ↓
More hours you work, more $ you make
What’s k?
hourly wage

3. Inverse Variation “y varies inversely as x”
“y is inversely proportional to x”
As x ↑, y ↓ or As x ↓, y ↑
Higher your speed while driving, less time it takes to get there
What’s k?
distance

4. Joint Variation Same as direct but more than 1
“y varies jointly as x and z”
“y is jointly proportional to x and z”

5. Combined Variation Both direct & inverse
“y varies directly as x and inversely as z”
“y is directly proportional to x and inversely proportional to z”

6. Example 1
The Work (w), measured in foot-pounds, required to stretch a spring x feet beyond its natural length varies directly as the square of x. If w = 20 ft-lbs when x = 2, find w when x = 3.

7. Example 2
Height (h) of a cylinder varies inversely as the square of the radius r. If height is 9 m when radius is 4 m, find height of cylinder whose radius is 2 m.

8. Example 3
Suppose z varies jointly as x and t2 and inversely as 3w – 1. If z = 4 when x = –2, t = 1, and w = 5, find z when x = –3, t = 4, and w = –1.

9. Homework
#409 Pg – 28 all, 30, 32, 34