Exploring distance time graphs
Exploring distance time graphs

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Exploring distance time graphs

1.4.6 Graphical conversions: So what is the relationship between the two scales?

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 vertical axis of Figure 12 is changed by subtracting 32 from each number to produce a new scale. This is illustrated in Figure 14. The Fahrenheit scale and the new scale are very simply related by the formula:

new scale = Fahrenheit scale – 32

This change of scale on the vertical axis does not affect the gradient.

Figure 14
Figure 14 Subtracting 32 from the vertical scale

You can see that, whereas the Fahrenheit scale goes from 32 to 212, the new scale goes from 0 to 180. Now a new straight-line graph can be drawn, as in Figure 15, which goes through the point (0,0) at one end and the point (100,180) at the other. You can work out the directly proportional relationship between the Celsius scale and the new scale by finding the gradient. The relationship is:

value on new scale = gradient x value on Celsius scale.

Figure 15
Figure 15 A directly proportional relationship
MU120_3

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has over 40 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to university level study, find out more about the types of qualifications we offer, including our entry level Access courses and Certificates.

Not ready for University study then browse over 900 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus