Direct proportion

We have learnt that the equation of a straight line has the form $y = mx + c$ , where $y$ and $x$ are variables and $m$ and $c$ are constants.

In the case where $c = 0$ we are left with the equation $y = mx$ .

When $y = mx$ then $y$ and $x$ are directly proportional to each other.

Being in direct proportion means the value of $y$ and $x$ increase or decrease by the same factor. If $x$ is doubled then $y$ is also doubled. If $x$ is reduced by a third then $y$ reduces by a third.

Let’s look at an example. $y = 2x$ . The values of $x$ and $y$ for $x = 1$ to $5$ are shown below.

If $x$ is doubled from $1$ to $2$ then $y$ is doubled from $2$ to $4$ .

If $x$ is increased by a factor of $2.5$ from $2$ to $5$ then $y$ is increased by the same factor from $4$ to $10$ .

Graphs of $y = mx$ go through the origin.

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