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What Are the Parts of a Graph? (Mathematics Lesson)

The Parts of a Graph

A graph is used to plot points, lines and curves.

The most common type of graph has 2 axes at right angles to each other.

For example, a Cartesian coordinate graph has an x-axis and a y-axis.



The main parts of the graph are:

The X-Axis

The x-axis is the horizontal axis on a graph.

The image below shows what we mean by the x-axis:



The x-axis is labelled with numbers (0, 1, 2, 3...) so you can measure how far across the x-axis a point is.

The Y-Axis

The y-axis is the vertical axis on a graph.

The image below shows what we mean by the y-axis:



The y-axis is labelled with numbers (0, 1, 2, 3...) so you can measure how far up the y-axis a point is.

The Origin

The x-axis and the y-axis are at right angles to one another and cross at a point called the origin.

The image below shows what we mean by the origin:



At this point the value along the x-axis is 0 and the value along the y-axis is 0. The Cartesian co-ordinate of the origin is (0,0).

The origin is often denoted by the letter O.

Putting It Together

The slider below shows how to draw a graph by putting the parts of a graph together.
Interactive Widget
Here is an interactive widget to help you learn about graphs.
Interactive Test
  show
 


Here's a second test on the parts of a graph.
Here's a third test on the parts of a graph.
Note

Why Use Graphs?

Graphs are often used in mathematics to plot functions.

Graphs can be very important in real life too. People often want to know the relationship between two things.

For example, a scientist may be interested in how quickly a material heats up. He may heat a material, and measure its temperature at different times.

A simple way of expressing this relationship would be to plot a graph of temperature against time:



The axes are labelled with the quantity they are measuring, and the units of that quantity.

In scientific graphs, the y-axis is used for the dependent variable - the output of the experiment. This is the thing the scientist is trying to measure; in this case, temperature.

The x-axis is used for the independent variable - the input of the experiment. This is the thing that is allowed to change to see if it affects the dependent variable; in this case, time.

Four Quadrants

The x and y-axes can have positive and negative values.

This means there are four quadrants made by the two axes.



Label the Axes!

It is very important to label the x-axis with an x and the y-axis with a y!

When graphs are used to plot relationships found in the real world, label the axes with what quantity they represent (temperature and time, for example) and also the units of those quantities (°C and s).

Pronouncing Axes

The word 'axes' is the plural of axis. It is pronounced "ax-eez", not "ax-ez".

In mathematics, a pair of axes should not make you think of this: