<p>Choose transformed variables X and Y to obtain a straight-line relationship.</p>
<div class="content-box-placement content-box-placement--full content-box-placement--align-center" style="display:flex;justify-content:stretch;max-width:100%"><div class="content-box content-box--emphasis" data-content-box-preset="emphasis" style="box-sizing:border-box;border-color:var(--content-box-border, #1E6FBA);border-style:solid;border-width:0px;border-radius:0px;background-color:var(--content-box-background, #F5F8FC);color:var(--content-box-foreground, #111827);padding:12px 16px;font-family:'EB Garamond', serif;font-size:16px;line-height:1.35;width:100%;max-width:100%;border-left-width:3px"><p style="text-align: center">\(Y=mX+c\qquad m=\dfrac{\Delta Y}{\Delta X}\)</p></div></div>
<p>\(m\) is the gradient; \(c\) is the value of \(Y\) when&nbsp;\(X=0\). Both are constants.</p>
<p>Label each axis with the transformed quantity and its units.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="graph-block" data-graph-config="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" data-width="210" data-height="150" data-proportional style="width:210px;height:150px;max-width:100%;display:flow-root;margin:0 auto;--graph-width:210px;--graph-aspect:210 / 150;"></div><p>\(y=3x^2+1\) plotted against \(x\): a curve.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="graph-block" data-graph-config="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" data-width="210" data-height="150" data-proportional style="width:210px;height:150px;max-width:100%;display:flow-root;margin:0 auto;--graph-width:210px;--graph-aspect:210 / 150;"></div><p>The same law plotted against \(X=x^2\): the straight line \(Y=3X+1\), gradient \(3\), intercept \(1\).</p></div></div></div>

Choose transformed variables X and Y to obtain a straight-line relationship.

\(Y=mX+c\qquad m=\dfrac{\Delta Y}{\Delta X}\)

\(m\) is the gradient; \(c\) is the value of \(Y\) when \(X=0\). Both are constants.

The Linear Form Y = mX + c

The Linear Form Y = mX + c