4.7 Variation

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

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

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

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”

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.

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.

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.

Homework #409 Pg. 262 21 – 28 all, 30, 32, 34