Sometimes you are told that 2 quantities (or values) are directly proportional (or inversely proportional) to one another. This means that there is a relationship between the two quantities; and because we have a relationship, we can write this as an equation.

Therefore, if you have a problem to solve, that involves direct or inversely proportiona quatities, you can use the equation to calculate your unknown quantity.

The figure below shows the general graphical representation of direct and Inverse proportions.

Directly Proportional

This means that if we calculate ‘k’ then we can solve problems of direct proportionality. Examples below

EXAMPLE 1

Problem Statement
STEP 1 — Find ‘k’

Now that we know the value for ‘k‘; replace it in the formula y = kx; we get y = 3x

STEP 2 — FInd ‘y’

EXAMPLE 2

Problem Statement
Find ‘F’

Inversely Proportional

EXAMPLE 3

EXAMPLE 4

Sometimes the relationship is not explicitly stated; so you have to look carefully at the problem statement you are given and determine whether you have a direct or inverse proportion between your given quantities. For example:

Finding the Coordinates of the Turning Point
Part (I) - Quartiles & Interquartile Range