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128 lines
6.3 KiB
HTML
128 lines
6.3 KiB
HTML
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<title>General Form of Equation of a Line</title>
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<h1>General Form of Equation of a Line</h1>
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<h3 align="center"><br />
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The "General Form" of the equation of a straight line is:<br />
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<br />
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</h3>
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<div class="center80">
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<p align="center" class="largest">Ax + By + C = 0</p>
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<p>
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A or B can be zero, but not both at the same time. </p>
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<div align="center"></div>
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<p>The General Form is not always the most useful form, and you may prefer to use:</p>
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<table border="0" align="center">
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<tr>
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<td class="larger"><p>The <a href="../equation_of_line.html">Slope-Intercept Form</a> of the equation of a straight line:</p>
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<p align="center"><span class="largest">y = mx + b</span></p></td>
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<td><img src="images/y-mxpb-graph.svg" width="120" alt="Slope-Intercept Form" /></td>
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</tr>
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<tr>
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<td class="larger"><div align="center"><i>or</i></div></td>
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<td> </td>
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</tr>
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<tr>
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<td class="larger"><p>The <a href="line-equation-point-slope.html">Point-Slope Form</a> of the equation of a straight line:</p>
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<p align="center"><span class="largest">y − y<sub>1</sub> = m(x − x<sub>1</sub>)</span></p></td>
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<td><img src="../data/images/graph-point-slope-a-sm.gif" alt="Point-Slope Form" width="120" height="98" /></td>
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</tr>
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</table>
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<p> </p>
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<div class="example">
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<h3>Example: Convert 4x − 2y − 5 = 0 to Slope-Intercept Form</h3>
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<p>We are heading for:</p>
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<p align="center"><span class="large">y = mx + b</span></p>
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<div class="tbl">
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<div class="row"><span class="left">Start with:</span><span class="right">4x − 2y − 5 = 0</span></div>
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<div class="row"><span class="left">Move all except y to the right:</span><span class="right">−2y = −4x + 5</span></div>
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<div class="row"><span class="left">Divide all by (−2):</span><span class="right">y = 2x − 5/2</span></div>
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</div>
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<p>And we are done! (Note: <b>m </b>= 2 and <b>b </b>= −5/2)</p>
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</div>
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<h2>Why Use It?</h2>
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<p>It has the advantage of working well with <b>vertical lines</b>, which the <a href="../equation_of_line.html">Slope-Intercept Form</a> and <a href="line-equation-point-slope.html">Point-Slope Form</a> do not.</p>
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<p> </p>
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<div class="related">
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<a href="../gradient.html">Slope (Gradient) 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="../data/straight_line_graph.html">Explore the Straight Line Graph</a>
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