# 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.

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.