**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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