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Direct proportionality
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Inverse proportionality

Direct Proportionality

Direct proportion
$y=3x$
Direct proportionality is a technique we can use to deal with variables which, when graphed, give a straight line which goes through $(0, \ 0)$ or the origin, as shown in the figure.

There are two common ways of posing problems like this:
  1. $A$ is directly proportional to $B$.
  2. $A$ varies directly as $B$.
These two sentences mean exactly the same thing.

There are several methods for dealing with direct proportionality and we will examine two of them here. The first is the most self-explanatory and uses tables, much as we did in the last section; the second uses more complex notation, but ultimately more generally useful as the problems become more difficult.

There is no difference apart from the language used between the work we did in the Unitary Method section, but you need to be familiar with this language for later.

If two quantities are described as being in direct proportion, they can be considered as ratios, and we can solve the problems using a table of values.

However, it is often useful to find the formula for the connection between variables, after which, finding several values is made much simpler. The following method is quite confusing to begin with, but with practice, it can be mastered.