<p>The table below shows experimental values of two variables \(x\) and \(y\) which are related by the equation \(y = ax^b\), where&nbsp;\(a\) and \(b\) are constants.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 490px;"><colgroup><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">\(x\)</th><th style="text-align: center; --cell-justify: center">\(1.5\)</th><th style="text-align: center; --cell-justify: center">\(2\)</th><th style="text-align: center; --cell-justify: center">\(2.5\)</th><th style="text-align: center; --cell-justify: center">\(3\)</th><th style="text-align: center; --cell-justify: center">\(4.5\)</th><th style="text-align: center; --cell-justify: center">\(6\)</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(y\)</td><td style="text-align: center; --cell-justify: center">\(45\)</td><td style="text-align: center; --cell-justify: center">\(25\)</td><td style="text-align: center; --cell-justify: center">\(15.8\)</td><td style="text-align: center; --cell-justify: center">\(11\)</td><td style="text-align: center; --cell-justify: center">\(5\)</td><td style="text-align: center; --cell-justify: center">\(2.6\)</td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Plot a straight line graph of \(\lg y\) against \(\lg x\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Use your graph to estimate the value of \(a\) and of \(b\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">On the same diagram, draw the line representing the equation \(y = x^3\) and hence find the value of \(x\) for which \(x^{3-b} = a\).</span></div></li></ol>
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The table below shows experimental values of two variables \(x\) and \(y\) which are related by the equation \(y = ax^b\), where \(a\) and \(b\) are constants.

Plot a straight line graph of \(\lg y\) against \(\lg x\).

Use your graph to estimate the value of \(a\) and of \(b\).

On the same diagram, draw the line representing the equation \(y = x^3\) and hence find the value of \(x\) for which \(x^{3-b} = a\).

Linear Law

Question 3ebb689e