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213 lines
8.1 KiB
HTML
213 lines
8.1 KiB
HTML
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<meta http-equiv="content-type" content="text/html; charset=utf-8">
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<title>Gradient (Slope) of a Straight Line</title>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Gradient (Slope) of a Straight Line</h1>
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<p class="center">The Gradient (also called <a href="geometry/slope.html">Slope</a>) of a straight line shows <b>how steep</b> a straight line is.</p>
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<h2>Calculate</h2>
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<p>To calculate the Gradient:</p>
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<div class="center80">Divide the <b>change in height</b> by the <b>change in horizontal distance</b></div>
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<table style="border: 0; margin:auto;">
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<tr>
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<td class="large"><b>Gradient</b> = <span class="intbl"><em>Change in Y</em><strong>Change in X</strong></span></td>
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<td style="width:20px;"> </td>
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<td><img src="algebra/images/slope.svg" alt="gradient" /></td>
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</tr>
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</table>
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<p>Have a play (drag the points):</p>
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<script src="geometry/images/geom-line-equn.js"></script>
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<script>geomlineequnMain('slope');</script>
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<h2>Examples:</h2>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="images/gradient1.gif" width="144" height="143" alt="gradient 3/3" /></td>
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<td> </td>
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<td><p>The Gradient = <span class="intbl large">
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<em>3</em>
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<strong>3</strong>
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</span> = 1</p>
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<p><b>So the Gradient is equal to 1</b></p></td>
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</tr>
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</table>
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<p> </p>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="images/gradient3.gif" alt="graph" width="147" height="145" align="left" /></td>
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<td> </td>
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<td><p>The Gradient = <span class="intbl large">
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<em>4</em>
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<strong>2</strong>
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</span> = 2</p></td>
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</tr>
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<tr class="center">
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<td colspan="3">The line is steeper, and so the Gradient is larger.</td>
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</tr>
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</table>
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<p> </p>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="images/gradient2.gif" width="152" height="150" align="left" alt="gradient 3/5" /></td>
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<td> </td>
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<td><p>The Gradient = <span class="intbl large">
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<em>3</em>
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<strong>5</strong>
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</span> = 0.6</p></td>
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</tr>
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<tr class="center">
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<td colspan="3">The line is less steep, and so the Gradient is smaller.</td>
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</tr>
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</table>
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<p class="center"> </p>
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<h2>Positive or Negative?</h2>
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<p>Going from left-to-right, the cyclist has to <b>P</b>ush on a <b>P</b>ositive Slope:</p>
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<p class="center"><img src="geometry/images/slope-neg.svg" alt="negative slope" /> <img src="geometry/images/slope-0.svg" alt="zero slope" /> <img src="geometry/images/slope-pos.svg" alt="positive slope" /></p>
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<p>When measuring the line:</p>
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<ul>
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<div class="bigul">
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<li>Starting from the left and going across <b>to the right is positive</b><br>
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(but going across to the left is negative).</li>
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<li><b>Up is positive</b>, and down is negative</li>
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</div>
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</ul>
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<p class="center"> </p>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="images/gradient4.gif" width="142" height="142" align="left" alt="gradient -4/2" /></td>
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<td> </td>
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<td><p>Gradient = <span class="intbl large">
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<em>−4</em>
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<strong>2</strong>
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</span> = −2</p></td>
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</tr>
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</table>
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<div class="center">
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<p>That line goes <b>down</b> as you move along, so it has a negative Gradient.</p>
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</div>
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<h2>Straight Across<br></h2>
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<div class="center">
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="images/gradient5.gif" width="143" height="143" align="left" alt="gradient 0/5" /></td>
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<td> </td>
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<td><p>Gradient = <span class="intbl large">
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<em>0</em>
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<strong>5</strong>
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</span> = 0</p>
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</tr>
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</table>
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</div>
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<p class="center">A line that goes straight across (Horizontal) has a Gradient of zero.</p>
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<h2>Straight Up and Down</h2>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="images/gradient6.gif" width="144" height="143" align="left" alt="gradient 3/0" /></td>
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<td> </td>
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<td><p>Gradient = <span class="intbl large">
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<em>3</em>
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<strong>0</strong>
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</span> = <span class="large">undefined</span></p>
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</tr>
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</table>
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<p class="center">That last one is a bit tricky ... you can't <a href="numbers/dividing-by-zero.html">divide by zero</a>,<br>
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so a "straight up and down" (vertical) line's Gradient is "undefined".</p>
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<h2>Rise and Run</h2>
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<p>Sometimes the horizontal change is called "run", and the vertical change is called "rise" or "fall":</p>
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<p class="center"><img src="algebra/images/graph-rise-run.svg" alt="rise and run" /></p>
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<p>They are just different words, none of the calculations change.</p>
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<p> </p>
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<div class="questions">
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<script>getQ(2068, 2069, 2070, 2071, 2072, 5316, 5317, 5318, 5319, 5320);</script>
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</div>
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<div class="related">
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<a href="equation_of_line.html">Equation of a Straight Line</a>
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<a href="y_intercept.html">Y Intercept of a Straight Line</a>
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<a href="quiz/linear_equation_test.html">Test Yourself</a>
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<a href="straight-line-graph-calculate.html">Straight Line Graph Calculator</a>
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<a href="data/graphs-index.html">Graph Index</a>
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