Åk 6–9

4.3 Proportionality
In order for a relation to be proportional two things must be met:

  • it must be a linear relation between only two variables, in other words the function value much increase or decrease evenly the entire time
  • the function graph should be a straight line that goes through the origin.

When either of these is met, then the relation is proportional.  A simple way to see this is naturally in a coordinate system.  Then you can directly see if the line is straight and goes through the origin.

Here you see two functions.  Both the fuctions’s graphs are straight lines.  However, its is only the first line with goes through the origin, and it is only that one that show a proportional relation.

If you don’t have a line in a coordinate system but only have the function given as a formula, you can still determine if the relation is a proportionality. Then the following demands must be fulfilled:

  • the variables may only depend on each other.
  • the function may not have a constant, in other words the c-value must be 0.

We take three function examples:

You can learn more about proportionality in the section Sequences and Proportionalities.