<h3>Solving linear equations</h3><p>A <strong>linear equation</strong> has the unknown only to the first power. To solve <code>2x + 3 = 11</code>, subtract 3 from both sides to get <code>2x = 8</code>, then divide by 2 to get <code>x = 4</code>. Always keep both sides balanced.</p><h3>Gradient</h3><p>The <strong>gradient</strong> (slope) measures steepness. Between points (x1, y1) and (x2, y2) it is <code>m = (y2 - y1) ÷ (x2 - x1)</code>. A line through (1, 2) and (3, 8) has gradient <code>(8 - 2)/(3 - 1) = 3</code>.</p><h3>The equation y = mx + c</h3><p>Every straight line can be written as <code>y = mx + c</code>, where <strong>m</strong> is the gradient and <strong>c</strong> is the y-intercept (where the line crosses the y-axis).</p><div class="callout"><strong>Kenyan context:</strong> A boda boda rider charges KSh 50 to board plus KSh 30 per kilometre. The fare is <code>y = 30x + 50</code>, where x is the distance. Here the gradient 30 is the cost per kilometre and the intercept 50 is the boarding charge. For a 6 km trip the fare is <code>30 x 6 + 50 = KSh 230</code>.</div>