Linear Law - Plotting Linearised Data and Lines of Best Fit
Linear Law - Plotting Linearised Data and Lines of Best Fit
The table below shows experimental values of two variables \(x\) and \(y\).
| \(x\) | \(0.5\) | \(1.0\) | \(1.5\) | \(2.0\) | \(2.5\) |
|---|---|---|---|---|---|
| \(y\) | \(1.20\) | \(1.00\) | \(0.87\) | \(0.76\) | \(0.66\) |
It is known that \(x\) and \(y\) are related by the equation of the form \(y = \frac{m}{x + n}\), where \(m\) and \(n\) are constants.
Using a suitable scale, plot the graph of \(\frac{1}{y}\) against \(x\).
- Use your graph to estimate the value of \(m\) and of \(n\).
- By drawing a suitable straight line, find the value of \(x\) and of \(y\) which satisfy the following pair of simultaneous equations.
\(y = \frac{m}{x + n}\)
\(y = \frac{10}{15x - 4}\)
Solution:
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Answer:(i) \(m\approx2.99,\ n\approx1.97\). (ii) \(x\approx0.91,\ y\approx1.04\), using the displayed best-fit line.
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