Direct and Inverse Variation

Day 2

y =kx with k≠0.

The general equation for direct variation is

k is called the constant of variation.

General Equation

If y varies directly as x, and y=24 and x=3 find the constant of variation.

y=kx24=k⋅3k=8

Example

Exampley varies directly as x, and x=8 when y=9. Find the constant of variation.

y = kx

9 = 8k

k = 9/8

y varies directly as x, and x=8 when y=9. Find y when x = 4.

Use the formula for direct variation.

Y = 4.5

Example

Inverse Variation

y varies inversely as x if k≠0

such that xy=k or

y=kx

Just as with direct variation, a proportion can be set up solve problems of indirect variation.

Indirect Variation

Lets do an example that can be solved by using the equation and the proportion.

x1y1 =x2y2

Solve:

Find x when y=27, if y varies inversely as x and x=9 when y=45.

Answer: 15

Determine if the chart is a direct variation

• To solve, find the constant of variation for each pairing of numbers using the formula y=kx.

• YES! The constant of variation is 2.

x 10 12 14 16 18

y 20 24 28 32 36

Determine if the chart is a direct variation

• To solve, find the constant of variation for each pairing of numbers using the formula y=kx.

• YES! The constant of variation is 1/2.

x 20 16 12 8 4

y 10 8 6 4 2

Determine if the chart is a direct variation

• To solve, find the constant of variation for each pairing of numbers using the formula y=kx.

• NO! The constant of variation is changes and is not the same for all pairs.

x 6 9 15 18 24

y 2 3 5 9 12

Determine if the charts are direct variationsx 2 8 9 14 18

y 6 24 27 42 54

x -3 9 15 18 -21

y -2 6 10 12 -14

x -1 3 5 8 10

y -2 6 10 12 -14