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Solving for a Direct Relationship (Literal Equations)

direct variation, literal equations, independent variable, dependent variable

A direct relationship:  is one where a change in one variable has an effect on another variable.  An example of direct relationship is

y=2x

Here, you see that a change in the independent variable [x] has a direct effect in the change on the dependent variable [y].  Here, y is two times the value of x.  However, often times, it may not be readily apparent what the relationship is.  So, the following example illustrates this point.

Example:

3y/4=x/2

Multiplying both sides by 4, we get:

4*(3y/4)=(x/2)*4
3y=(2x)

Lastly, dividing both sides by 3, we get:

3y/3=(2x)/3

which becomes:

y=(2x)/3 or y=(2/3)x

So, in the final result here, we see the direct relationship that y is two thirds of whatever the value of x maybe

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