Linear function (calculus): Difference between revisions

Revision as of 19:30, 18 June 2013

Revision as of 19:38, 18 June 2013

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<li>To use the function or graph the line, the coefficient letters <em>a</em> and <em>b</em> must be given as actual real numbers. For example: <math>y(x)=2x-1</math>. Here <em>a</em>=2 and <em>b</em>=-1.</li>

<li>In the function, <em>x</em> is the independent variable and <em>y</em> is the dependent variable.</li>

<li>The [[/Domain_(mathematics)Domain_of_a_function|___domain]] or set of allowed values for <em>x</em> of a linear function is &nbsp;<math>\Re</math>&nbsp; (all real numbers). This means that any real number can be substituted for <em>x</em>. (Of course, the value of <em>y</em> depends on the substituted value for x.)</li>

<li>The set of all points: (<em>x</em>,<em>y</em>(<em>x</em>)) is the line.</li>

<li>Since two points determine a line, it is enough to substitute two different values for <em>x</em> in the linear function and determine <em>y</em> for each of these values (see videos below).</li>

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<li>The general form of a line is a [[linear equation]]; the opposite is not necessarily true. </li>

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<tr><td valign="top">Example: 3<em>x</em>-2<em>y</em>=1 and 6<em>x</em>-4<em>y</em>=2 are the same linear function, i.e. their graph is the same line.

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<li>This form of a linear function can easily be extended to lines in higher dimensions, which is not true of the other forms. </li>

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