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.
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