# Linear relationships

There is a linear relationship between two variables if the relationship between them can be represented by a line or part of a line. In other words variables have a linear relationship if one can be given by the other, by multiplying, dividing, adding or subtracting. In the above, k and b are constants.

Example 1

The price of potatoes is €0.80 / kg. How much does 5 kg cost?

Give the function y for potatoes when buying x kilos of potatoes.

Solution the function when buy x kilos of potatoes The graph of the function is straight line. We can also read from the graph that 5 kg of potatoes costs €4. Example 2

A taxi fare consists of an €8 departure fee and a €0.5 kilometre rate. Create a function for the cost of a taxi against a function of the distance. Draw a graph of the function.

Solution

We mark the taxi fare with y and the kilometres travelled with x  How many kilometres can we travel with €20? We can read the information from the graph, which shows that a 24 kilometre journey costs €20. Turn on the subtitles if needed