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Linear Graphs

Linear or straight line graphs are commonly used during the analysis of experimental data to represent relationships between real life variables. One reason for this is that experimental measurements often contain a lot of 'noise', due to unknown factors, so it would not be sensible to use complicated curves to represent relationships when the data itself is imprecise. Another reason is that linear graphs have important and well understood characteristics.

This section examines the important features of linear graphs.

Try the following questions to refresh your memory and check your skills. If you have any difficulty follow the underlined links for further information.

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Self-Test

Questions
1. A farmer drives a tractor at the same speed most of the time when ploughing fields and suspects that the amount of diesel used is related to the amount of time ploughing. The data below shows the relationship between fuel used and ploughing time. Where would you draw a "line of best fit" to represent this relationship?

2. What are the gradients of the lines below?

3. State the gradients and y-intercepts of the lines below:
  • $y=2x-1$
  • $y=2-3x$
  • $x+2y=6$