Inverse Variation If y varies inversely as x, then Example 2 Graph y

9.1 Direct, Inverse, Joint, and Combined Variation (work).notebook

9.1 Direct, Inverse, Joint, and Combined Variation

RECALL from Algebra 1: Direct Variation

If y varies directly as x, then y = kx.

Example 1

The variable y varies directly as x,

and y = 6 when x = 2.

a) Find the constant of variation.

b)Write the appropriate inverse variation equation.

c) Find y when x is 21 , 1, and 2.

Inverse Variation

If y varies inversely as x, then y = xk .

Example 2

Graph y = 1x .

April 26, 2017

9.1 Direct, Inverse, Joint, and Combined Variation (work).notebook

April 26, 2017

Example 3

The variable y varies inversely as x,

and y = 6 when x = 3.

a) Find the constant of variation.

b)Write the appropriate inverse variation equation.

c) Find y when x is 21 , 1, and 2.

Joint Variation

If y varies jointly as x and z, then y = kxz.

Example 4

The variable y varies jointly as x and z,

and y = 16 when x = 4 and z = 21 .

a) Find the constant of variation.

b)Write the appropriate joint variation equation.

c) Find y when x = 2 and z = 41 .

9.1 Direct, Inverse, Joint, and Combined Variation (work).notebook

April 26, 2017

Combined Variation

Combined variation is any combination of

direct, inverse, and/or joint variation.

Ex: b varies jointly as c and e and inversely as d

b = kce

d

Example 5

Write a general equation for each.

a) y varies directly with b and inversely with c

b) z varies jointly as x and the cube root of z

c) h varies inversely as g and jointly as e and f

Example 6

The variable y varies jointly as x and z, and inversely

as w. If y = 72 when x = 6, z = 3, and w = 12 :

a) Find the constant of variation.

b) Write the appropriate combined variation equation.

c) Find y when w = 18, x = 14 , and z = 12.

9.1 Direct, Inverse, Joint, and Combined Variation (work).notebook

April 26, 2017

Example 7

The variable a varies directly as b, and inversely

as the square root of c. Ifa = 10 when b = 6 & c = 9:

a) Find the constant of variation.

b) Write the appropriate combined variation equation.

c) Find b when a = 20 and c = 4.

Example 8

The variable m varies jointly as j and the cube of p,

and inversely as n. If m = 30 when j = 5, p = 2, & n = 4:

a) Find the constant of variation.

b) Write the appropriate combined variation equation.

c) Find m when j = 4, p = 3, and n = 2.

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