# Direct Proportions

Two variables are directly proportional when one varibale is multiplied or divided one by any number, the other variable is also multiplied or divided by that same number.

y = kx.

**k** is the **constant of proportionality**.

The relation is commonly denoted as:

y ∝ x

The weight of a product and its price are directly proportional.

If 1 pound of tomatoes cost $2, 2 pounds will cost $4 and ½ pound cost $1.

y = 2x

The graph is a straight line that passes through the origin and its slope is the constant of proportionality.

#### Examples

A car travels 240 miles at a constant speed in 3 hours. How many miles will be travelled in 2 hours?

In this example, the distance and time are directly proportional, because when the distance increases, the total time increases and when the distance decreases, the total time decreases.

A grandfather shares $450 between his three grandchildren who are 8, 12 and 16 years of age. If he distributes the money in proportion to their ages, how much will each one receive?

In this example, the age and the money are directly proportional because the older the children are, the more money they will receive and the younger the children are, the less money they will receive.

Let x, y, z represent the amounts that each will receive.

For the properties of proportions:

Each grandchild will receive: