Direct and Inverse Proportion

In science, we constantly look for relationships between variables. When we change one thing , say, the temperature of a gas or the force on a spring , something else changes in response. Proportion describes the mathematical nature of that relationship.

Proportion: A relationship between two variables where a change in one produces a predictable, consistent change in the other.

There are two fundamental types of proportional relationship you need to master at MYP 5:

• Direct proportion , as one variable increases, the other increases in a consistent way
• Inverse proportion , as one variable increases, the other decreases in a consistent way

Understanding proportion is not just a maths skill , it is central to interpreting experimental data, drawing graphs, and making predictions in every branch of science.

Direct Proportion: Two variables are in direct proportion if, when one variable is multiplied by a factor, the other variable is multiplied by the same factor. Their ratio remains constant.

If $y$ is directly proportional to $x$, we write:
$y\propto x$

This means:
$\frac{y}{x}=k\text{(a constant)}$

or equivalently:
$y=kx$

where $k$ is called the constant of proportionality.

Key features of direct proportion:

• If $x$ doubles, $y$ doubles
• If $x$ triples, $y$ triples
• If $x$ is halved, $y$ is halved
• The ratio $\frac{y}{x}$ is always the same value
• The graph of $y$ against $x$ is a straight line through the origin