Constant of Proportionality

A direct variation is represented by a ratio or equation :

kx

y or kxy k ≠ 0

Direct Variation – constant ratio

EX1)

x 1 2 3 4y 3 6 9 12

Determine if the table represents a direct variation. If so, state the constant of proportionality

Step 1 Substitute values for variables

1

3

x

y

K =

2

6

3

9

4

12

3 3 3 3

Step 2 Simplify

This is a direct variation because the ratios are constant. The constant of proportionality is 3.

EX2) Identify the constant of proportionality in the equation y=15x where

y = 15 x

k = constant of proportionalityy = k x

15 = constant of proportionality

Explain the relationship. y = cost of concert tickets and x = number of concert tickets

Each concert ticket cost $15.

EX3) Refer to the graph. Is there a direct variation? Explain

0 1 2 30

2

4

6

8

pounds

$

There is not a direct variation.

The line does not go through the origin.

notes

Constant of Proportionality

Date ____________

A direct variation is represented by a ratio or equation :

Direct Variation –

EX1)

xy

Determine if the table represents a direct variation.

Step 1

Step 2

EX2) Identify the constant of proportionality.

y = 15 x

k =

Explain the relationship.

y =

x =

EX3) Refer to the graph. Is there a direct variation? Explain

0 1 2 30

2

4

6

8

pounds

$