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Graphs are often used in everyday life to give information about how two quantities are related. The gradient and intercept of the graph can be interpreted from the graphs.

Before reading this guide, it may be helpful to read the guide for [graphs in real life from and the guide for .

Real life graphs

There are many situations where a graph can be useful to help find quantities. They usually involve working costs.

Example

The graph below shows the charges a hotel makes for parties in their function room.

They can cater for up to 50 guests, and the cost includes the charge for hiring the room.

Question

Ciara wants to hold a party for 30 guests. How much will it cost?

Solution

Follow the dashed line from 30 on the horizontal axis to meet the graph line, then follow across and read the value on the vertical axis. This gives 800.

It costs £800 for 30 guests.

Question

What does the intercept on the cost axis (£s) represent?

Solution

The intercept (where the graph crosses the vertical axis) is the cost when there are zero guests. This is the charge for hiring the room and is equal to £350.

Question

Find the gradient of the graph.

Solution

Question

What does the gradient represent when hiring the room?

Solution

The gradient means the cost per person when hiring the room. The cost per person is £15.