 The values of the x- and y-coordinates in a graph sometimes relate to measurements of physical quantities: for example, in graphs of height against distance, or temperature against time. Physical quantities always have units associated with them, and these must be shown on the axes’ labels of the graph.

In mathematics, however, values of x- and y-coordinates that have been calculated using a formula may simply be numbers: they may not have units atta
Author(s): The Open University

This section started by looking at conversion graphs which were straight lines passing through the origin of the graph. The intercept in those cases was zero, and only one number – the gradient – was needed to describe the relationship between the quantities plotted on the horizontal and vertical axes. In the more general case, the graph is still a straight line with a constant gradient, but the line no longer goes through the origin. An extra number – the intercept – is used to pin t
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To determine this, you first need to determine the gradient of the straight line inFigure 11.

The new vertical scale goes from 0 to 180 as the Celsius scale on the horizontal axis goes from 0 to 100. So the gradient is and the relationship between the scales on th
Author(s): The Open University

You know that if the line passes through the origin of a straight-line graph, then the gradient of the graph links the values on the horizontal and vertical axes. The general relationship is:

on vertical axis = gradient x value on horizontal axis

Now suppose the scale on the ve
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First you need some data about corresponding temperatures on each scale. In the case of Celsius and Fahrenheit, there are two fixed points of reference: the freezing and boiling points of water. On the Celsius scale, the freezing point is defined to be 0°C; on the Fahrenheit scale, the freezing point is 32°F. So if you plot degrees Celsius on the horizontal axis and degrees Fahrenheit on the vertical axis of a graph, the freezing point of water is represented by a point with the coordinates
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One of the main features of a straight-line graph is that the line has a constant slope. The gradient of the slope is numerically equal to the constant of proportionality. For a 1 : 25 000 map, the constant of proportionality between ground distances in kilometres and map distances in centimetres is 0.25 km per cm. So the gradient of the corresponding graph is 0.25.

A similar relationship holds for a 1 : 50 000 map. In this case, 1 cm on the map corresponds to 0.5 km on the ground, so t
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Look at Figure 9. Start with the map distance on the horizontal scale, move vertically up until you reach the line, then move horizontally until you reach the vertical axis. The number at that point will give you the corresponding ground distance in kilometres.

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This means, for instance, that if you double one value, the effect is to double the other, and if you third one value, the upshot is that the other is divided by three as well. And the fact that the relationship is directly proportional has an important consequence for the graph-it will necessarily be a straight line.

Only two points are needed to draw a straight-line graph. Choosing one of the points is straightforward, it is the origin of the graph. Why? Because zero distance on the m
Author(s): The Open University The time-series plot is the most frequently used form of graphic design. With one dimension marching along to the regular rhythm of seconds, minute, hours, days, weeks, months, years, centuries, or millennia, the natural ordering of the time scale gives this design a strength and efficiency of interpretation found in no other graphic arrangement.

(Tufte, E. (1983) The Visual Display of Quantitative Information, Gra
Author(s): The Open University

The main aim of this section is to give you practice in reading, interpreting and drawing a variety of graphs created for many different purposes.You will need graph paper for this section.

Graphs occur in all sorts of different contexts and applications. Graphical representations can be used to show profiles of height plotted against distance for sections of the Peak District walk, for example. This section looks at three sorts of graphs: time-series graphs, conversion graphs and mathe
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This Unit teaches on drawing and interpreting graphs. It has eight sections, each dealing between them with 4 different types of graph. You will need to draw some graphs, so make sure you have a flat surface to work on. You will also need to have centimetre graph paper and your calculator to hand as you study the material.

Section 3 is based on a video band, ‘Single-track minders’. This is split into four separate viewing sessions, each followed by an activity. You should expect to
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All representations (including graphical ones) rely on shared understandings of symbols and styles to convey meaning. Like maps, graphical representations stress some features and ignore others. As you work through this Unit, bear in mind that graphs are selective representations of information. When you come across different graphs ask yourself what is being stressed and what is being ignored.

In the newspapers, you are likely to find graphs used to present all sorts of information: ho
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After studying this Unit you should be able to:

• Explain in English and by using examples, the conventions and language used in graph drawing to someone not studying the course

• Use the following terms accurately, and be able to explain them to someone else: ‘time-series graph’, ‘conversion graph’, ‘directly proportional relationship’, ‘“straight-line” relationship’, ‘gradient’, ‘intercept’, ‘x-coordinate’, ‘y-coordinate’, ‘coor
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Graphs are a common way of presenting information. However, like any other type of representation, graphs rely on shared understandings of symbols and styles to convey meaning. Also, graphs are normally drawn specifically with the intention of presenting information in a particularly favourable or unfavourable light, to convince you of an argument or to influence your decisions.

This unit is from our archive and is an adapted extract from Open mathematics (MU120) which is no longer
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If you want to subtract without using a calculator, you need to know off by heart what you get if you subtract any number up to 10 from any bigger number up to 20. All the possible combinations are shown in the table below. Author(s): The Open University

A decimal number is a different way of representing numbers smaller than one. You put them after a full stop (the decimal point), for instance 0.5. The first digit after the decimal point represents tenths. If you sliced a cake into 10 slices, each slice would be a tenth of the cake. So 0.5 is the same as saying 5 tenths, and can be written Author(s): The Open University

In this section, you have learned about appropriate ways of interpreting data in tables. By working through examples, you have seen how it can be useful to calculate appropriate proportions and ratios, and to present some of the data in graphical form. Guidelines for the choice of graphics have been given. When the data in a table are in the form of counts, you have seen that it can be useful to calculate the counts in a particular row or column as proportions (usually in the form of percenta
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## Activity 3.1: Health care personnel in Thailand: calculating percentages

Would it be helpful, in considering possible changes in the way health care personnel are divided into the five categories listed, to recalculate the numbers in t
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In this section you have been introduced to some guidelines for presenting data in tables. These guidelines apply particularly when the data in a table are being used to illustrate a particular point or to show up clearly a particular pattern.

You have seen that, in some circumstances, following the second of these guidelines leads to some pooling together of rows. (In other cases, it could be columns or individual cells that are pooled.) However, care is needed when, by making such sim
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