What is a proportional relationship? A percentage relationship is an exact proportion. It s a equation that shows two proportions where one can be derived entirely from the other, like cost of living to income. A proper proportion between two factors of equal values can be used to express a relationship. That is why we can say that the relationship between cost of living and income is a proportional relationship.

Let us take an example. If we take cost of living first and income last, then we can say that the cost-to-income relation is called the cot-cos (or cost-to-house-value) relationship. This can also be expressed as the cot-dec (or cost-to-income-ratio). The cot-dec relationship tells us the percentage of income that goes to pay fixed expenditures like taxes and retirement contributions.

On the other hand, the cot-cos relationship tells us that the percentage of expenditure that goes to fixed expenditures like buying groceries or paying the mortgage interest. These fixed expenses cannot be changed at will, so their values must be fixed too.

## How to find out proportion relationships / what is a proportional relationship ?

How do we find out what these constant proportion relationships are? We could use various methods such as graphing, calculus, etc. However, there is another way of finding out relationship equities that is not based on any of the known methods. This is by using stochastic, random walks, and logistic function equations. In fact, there are even some textbooks that describe and illustrate how to solve different problems using this method.

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#### Problems

The problem arises when we wish to express a relationship between two quantities, say cost of living and income. Often, a relationship will look like this: cost of living (C.L.R.) times net income (N.I. ), where the first term is always positive and the second term is always negative. A suitable inverse proportion would then be equal to the sum of the first term and minus the second term.

### How to solve the proportional relationship

#### First Way

The basic way of solving this problem is to plot a graph, called a parabola on a chart. We then wish to determine the slope of this parabola on the horizontal line representing the gross monthly expenditure or income and the corresponding figure for the reverse side of the graph. This can be done by plotting a line connecting the two points on the graph. We now have a good idea of the slopes of the curves relating the two quantities.

#### Second Way

One more way of finding out what is the relation between two ratios is to examine what is called a parabola in a graphical study. The parabola can be plotted on any graph and a suitable constant can then be plotted on the graph.

By plotting the parabola on the chart, we then get a graphical representation of the proportion between the two terms. Here the intercept relation will be most useful as it gives us the measure of how far one party is ahead of the other in the income or expenditure game.

#### Importance

The importance of this relationship cannot be underestimated. The fact that it is possible to plot a parabola on a chart means that we are now able to plot a comparable graph for almost any quantity. In addition to this, it is possible to examine any other quantity such as the values of the mean and standard deviation.

An important thing to note here is that if two quantities differ in sign, then they are positively related to one another. In other words, if one quantity is bigger than the other by more than a small percentage then they are positively related. Equations can then be written for any quantity to evaluate it as the difference between the mean value and the standard deviation value.

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#### Conclusion

This may seem confusing but once you learn the concepts of proportional relations, it starts to make a lot more sense. It is important to remember however that one does not have to learn how to plot a parabola on a graph, but rather how to solve a problem associated with a proportional relation.

For example, if you want to know what is the constant of proportionality. Then all you need to do is plot your data on a chart and you will then be able to evaluate the relationship between the two quantities.

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