<p>The table below shows experimental values of two variables \(x\) and \(y\).</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 420px;"><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;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">\(x\)</th><th style="text-align: center; --cell-justify: center">\(0.5\)</th><th style="text-align: center; --cell-justify: center">\(1.0\)</th><th style="text-align: center; --cell-justify: center">\(1.5\)</th><th style="text-align: center; --cell-justify: center">\(2.0\)</th><th style="text-align: center; --cell-justify: center">\(2.5\)</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(y\)</td><td style="text-align: center; --cell-justify: center">\(1.20\)</td><td style="text-align: center; --cell-justify: center">\(1.00\)</td><td style="text-align: center; --cell-justify: center">\(0.87\)</td><td style="text-align: center; --cell-justify: center">\(0.76\)</td><td style="text-align: center; --cell-justify: center">\(0.66\)</td></tr></tbody></table></div></div>
<p>It is known that&nbsp;\(x\) and \(y\) are related by the equation of the form \(y = \frac{m}{x + n}\), where&nbsp;\(m\) and \(n\) are constants.</p>
<p>Using a suitable scale, plot the graph of \(\frac{1}{y}\) against \(x\).</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Use your graph to estimate the value of \(m\) and of \(n\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">By drawing a suitable straight line, find the value of \(x\) and of \(y\) which satisfy the following pair of simultaneous equations.</span></div></li></ol>
<p style="text-align: center">\(y = \frac{m}{x + n}\)<br>\(y = \frac{10}{15x - 4}\)</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1775549390753-ag7pmkj47wl.png" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

The table below shows experimental values of two variables \(x\) and \(y\).

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.

\(y = \frac{m}{x + n}\)
\(y = \frac{10}{15x - 4}\)

Linear Law

Question cb6af03f