Straight-line explorer

<p>For a nonvertical line, \(y=mx+c\): \(m\) is its gradient and \(c\) is its y-intercept. Every point on the line satisfies its equation.</p>
<p>Given a point \((x_1,y_1)\) and gradient \(m\), substitute into \(y=mx+c\) to find \(c\). If two points are given, find the gradient first.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center">Feature</th><th style="text-align: center; --cell-justify: center">How to find it</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">x-intercept</td><td style="text-align: center; --cell-justify: center">Set&nbsp;\(y=0\).</td></tr><tr><td style="text-align: center; --cell-justify: center">y-intercept</td><td style="text-align: center; --cell-justify: center">Set&nbsp;\(x=0\).</td></tr><tr><td style="text-align: center; --cell-justify: center">Vertical line through a point</td><td style="text-align: center; --cell-justify: center">Its equation is \(x=\text{the point’s x-coordinate}\).</td></tr></tbody></table></div></div>
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<p>Two distinct points determine a straight line. Plot a third point as a check. The intersection of two lines satisfies both equations; check a graphical reading by substitution.</p>

For a nonvertical line, \(y=mx+c\): \(m\) is its gradient and \(c\) is its y-intercept. Every point on the line satisfies its equation.

Given a point \((x_1,y_1)\) and gradient \(m\), substitute into \(y=mx+c\) to find \(c\). If two points are given, find the gradient first.

Two distinct points determine a straight line. Plot a third point as a check. The intersection of two lines satisfies both equations; check a graphical reading by substitution.

Equations and intercepts

Equations and intercepts

Feature	How to find it
x-intercept	Set \(y=0\).
y-intercept	Set \(x=0\).
Vertical line through a point	Its equation is \(x=\text{the point’s x-coordinate}\).