Revision:Reduction to Linear Form

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Revision:Reduction to Linear Form

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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Reduction to Linear Form

In order to show that data from a science experiment fits a rule, we have to be able to plot two variables on a graph so that a straight line relationship results (this will be the line of best fit if the data is experimental).

In questions, you may be given some data and you may be asked to plot against $\displaystyle \frac{1}{x}$ .

If the data lies in a straight line, you know, from the equation of a straight line ( y = mx + c ), that $\displaystyle y = \frac{m}{x} + c$ , since $\displaystyle \frac{1}{x}$ is on the x-axis.

You have therefore found the relationship between the data.

Example

V	5	10	15	20	25
R	149	175	219	280	359

By drawing a graph, show that these pairs of values may be regarded as approximations to values satisfying a relationship of the form R = a + bV^2 .

In this question, you would plot against V^2 . If a straight line comes out, then you know that (from y = mx + c ) R = mV^2 + c (which is just the same as R = a + bV^2 , since and , and are just constants).

The second part of such a question may ask you to calculate the values of a and b. In this example, b is the gradient of the graph and a is the y-intercept (this can again be established by comparing the equation to y = mx + c ).