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In a directly proportional relationship, the values of x and the values along the y-axis (e.g., f(x)) "follow" each other. This means that:

• When the x-value is doubled, the f(x)-value is also doubled.
• When the x-value is halved, the f(x)-value is also halved.
• When the f(x)-value is doubled, the x-value is also doubled.
• When the f(x)-value is halved, the x-value is also halved.

A linear function is directly proportional if the graph passes through the origin (0,0). This means the equation of the function is of the form:

$\mathrm{f(x)}=ax+0$, which is often written simply as:

$\mathrm{f(x)}=ax$

The graph of a directly proportional function is a straight line.