<p>A straight line may be written in the general form \(ax+by=k\), where&nbsp;\(a\), \(b\) and \(k\) are constants, and \(a\) and \(b\) are not both zero.</p>
<p>When&nbsp;\(a\ne0\) and \(b\ne0\), rearranging gives&nbsp;\(y=-\dfrac{a}{b}x+\dfrac{k}{b}\). Hence the gradient is \(m=-\dfrac{a}{b}\).</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: left; --cell-justify: flex-start">Type of line</th><th style="text-align: left; --cell-justify: flex-start">Condition or equation</th><th style="text-align: left; --cell-justify: flex-start">Key feature</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">Uphill</td><td style="text-align: left; --cell-justify: flex-start">\(m&gt;0\)</td><td style="text-align: left; --cell-justify: flex-start">The line rises from left to right</td></tr><tr><td style="text-align: left; --cell-justify: flex-start">Downhill</td><td style="text-align: left; --cell-justify: flex-start">\(m&lt;0\)</td><td style="text-align: left; --cell-justify: flex-start">The line falls from left to right</td></tr><tr><td style="text-align: left; --cell-justify: flex-start">Horizontal</td><td style="text-align: left; --cell-justify: flex-start">\(a=0\), so \(y=\dfrac{k}{b}\)</td><td style="text-align: left; --cell-justify: flex-start">Gradient \(=0\)</td></tr><tr><td style="text-align: left; --cell-justify: flex-start">Vertical</td><td style="text-align: left; --cell-justify: flex-start">\(b=0\), so \(x=\dfrac{k}{a}\)</td><td style="text-align: left; --cell-justify: flex-start">Gradient is undefined</td></tr></tbody></table></div></div>
<p>A horizontal line has the same \(y\)-coordinate at every point, while a vertical line has the same \(x\)-coordinate at every point.</p>

A straight line may be written in the general form \(ax+by=k\), where \(a\), \(b\) and \(k\) are constants, and \(a\) and \(b\) are not both zero.

When \(a\ne0\) and \(b\ne0\), rearranging gives \(y=-\dfrac{a}{b}x+\dfrac{k}{b}\). Hence the gradient is \(m=-\dfrac{a}{b}\).

A horizontal line has the same \(y\)-coordinate at every point, while a vertical line has the same \(x\)-coordinate at every point.

Graphs of Linear Equations

Graphs of Linear Equations