### Intro to proportional relationships (video) | Khan Academy

Learn about and revise ratio, proportion and rates of change with this BBC Bitesize GCSE Maths Edexcel study guide. There are four steps to do this: write the proportional relationship; convert to an equation using a constant of. Most books say that a is directly proportional to b if and only if a = kb for some but taking the definition literally, it would seem to imply that any k will do, the term "directly proportional" is always applied to the relationship. The relationship can be linear, directly proportional, inversely proportional or non -linear. Linear just means that the two variables give a straight line graph.

Both the number of cans and the cost changed by the same factor, 2. Definition of Direct Proportion When quantities are related this way we say that they are in direct proportion. That is, when two quantities both change by the same factor, they are in direct proportion.

### Direct Proportions: What Are They? What Are They Used For?

In the above example the number of soup cans is in direct proportion to the cost of the soup cans. The number of soup cans is directly proportional to the cost of the soup cans. The formal definition of direct proportion: Two quantities, A and B, are in direct proportion if by whatever factor A changes, B changes by the same factor.

Half the volume of a liquid has half the weight.

Let us present another example of a direct proportion. The weight of a liquid is directly proportional to its volume. Suppose that you had a container holding 6 quarts of a liquid, and that liquid weighed 3 pounds. If we poured out half of the liquid so that only 3 quarts remained, that liquid would now weigh 1. So, in this example the weight and volume of the liquid are in direct proportion. Symbol for directly proportional is alpha.

Here is a shorthand way to say that the quantities A and B are directly proportional: The Greek letter between the A and the B is called alpha. It is here written in lower case script.

In this context it is shorthand for the phrase 'is directly proportional to. Whenever you have a direct proportion as stated above you can change it into an equation by using a proportionality constant.

Here is how the direct proportion would look as an equation: And so, or at least based on the data points we have just seen. So based on this, it looks like that we have a proportional relationship between y and x.

## Direct Proportion and The Straight Line Graph

So this one right over here is proportional. So given that, what's an example of relationships that are not proportional. Well those are fairly easy to construct.

So let's say we had-- I'll do it with two different variables. So let's say we have a and b. And let's say when a is one, b is three. And when a is two, b is six.

## Direct Proportion

And when a is 10, b is So here-- you might say look, look when a is one, b is three so the ratio b to a-- you could say b to a-- you could say well when b is three, a is one. Or when a is one, b is three.

So three to one. And that's also the case when b is six, a is two. Or when a is two, b is six. So it's six to two.

### Mathwords: Direct Variation

So these ratios seem to be the same. But then all of sudden the ratio is different right over here. This is not equal to 35 over So this is not a proportional relationship.

In order to be proportional the ratio between the two variables always has to be the same. So this right over here-- This is not proportional.