Patterns and Proportional Relationships

Direct Proportion

The table below is a linear function.

X 1 2 3 4

Y 8 16 24 32

One way to describe the function is as x increases by one, y increases by 8.

Another way to describe the function is by looking at the ratio y/x in each column of the table. In each column y/x = 8.

This can be written as the equation y = 8x

Any function (linear table) that can be written as y = kx, where k is a constant, is called a direct proportion.

Direct Proportion in a Graph

How can I determine if a graph is a direct proportion?

1. The graph of a direct proportion must be a straight line and pass through the point (0, 0).

2. Pick points on the graph and divide y by x. If the answer is a constant (k) each time, the graph fits the criteria for a direct proportion.

You try it!

Scout earns $12 an hour for each hour she works. Show that a direct proportion exists between the number of hours she works and the amount of money she earns.

Create a table using the information you have.

Write an equation representing the situation.

Does the equation for this problem fit the equation for a direct proportion y = kx ?

Indirect Proportion

An indirect proportion exists when the product (answer you get when you multiply) of two variables is a constant (k).

For example if the variables are x and y, an indirect proportion can be written as xy = k or as y = k/x.

The graph of an indirect proportion will never be a straight line.

Graph the following coordinate pairs

(1, 8) (2, 4) (4, 2) (8, 1) Is this a direct proportion or indirect

proportion? This graph is typical of an indirect proportion.

What happens when you multiply x and y? Each product equal 8, thus this is an indirect

proportion.

You try it! Is the function y = 4x + 2 a direct proportion?

1st step: if x = 1, y = ? (hint: make a table if it helps)

2nd step: what does this y/x = ?

3rd step: pick a second point. If x = 2, y = ? What does this y/x = ?

Did you get the same answer for step 2 and 3? If so it is a direct proportion, if not the function is not a direct proportion.