Proportional or direct relationships

A proportional or direct relationship is one where the value of one variable is directly related to the value of another.  For instance, a very simple direct relationship is:

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This relationship says that the value of y is always twice as big as the value of x.  This relationship could be described a number of ways:

·         The value of y varies with the value of x

·         The value of y is directly proportional to the value of x

A relationship is not a direct one if there are other terms in it as well, like this one for instance:


In order for a relationship to be proportional, you need to be able to write it in this general form:


‘k’ is called the constant of proportionality, and can be any value you need apart from zero.  In our original  equation, the constant of proportionality is ‘2’.

You can also have direct relationships where one variable varies as the square of the other variable, like this one for instance:


In this case we’d say that y varies directly as x2.  You can also have direct cubic relationships and so on…

Because there are no other terms in these equations, the graphs of any direct relationship are going to pass through the origin (0, 0) point of the graph.  Just look at any of the equations to confirm this – whether you’re talking about  or , when x equals 0, y is going to equal 0 too.