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Recognize the standard form of a linear function. Find at least two points. Plot the points. Connect the points.
Linear functions are typically written in the form f(x) = ax + b. The a represents the gradient of the line, which gives the rate of change of the dependent variable. This is also known as the "slope." The b represents the y-axis intercept. It is the value of the dependent variable y or, in other words, f(x) when x = 0. Say, for example, that you have a function f(x) = x + 5. This is a linear function in standard form. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/8\/85\/Do-Linear-Functions-Step-1Bullet1-Version-2.jpg\/v4-460px-Do-Linear-Functions-Step-1Bullet1-Version-2.jpg","bigUrl":"\/images\/thumb\/8\/85\/Do-Linear-Functions-Step-1Bullet1-Version-2.jpg\/aid4531126-v4-728px-Do-Linear-Functions-Step-1Bullet1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"<div class="mw-parser-output"><p>License: <a rel="nofollow" class="external text" href="https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/">Creative Commons<\/a><br>
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<\/p><\/div>"} You know your graph will be a straight line because you have a linear function; therefore, you really need only two points. In general, though, you should find three points instead, to check for accuracy. In the example above, you might choose to use -1, 0, and 1 for your x values. Solve as shown. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/7b\/Do-Linear-Functions-Step-2Bullet1-Version-2.jpg\/v4-460px-Do-Linear-Functions-Step-2Bullet1-Version-2.jpg","bigUrl":"\/images\/thumb\/7\/7b\/Do-Linear-Functions-Step-2Bullet1-Version-2.jpg\/aid4531126-v4-728px-Do-Linear-Functions-Step-2Bullet1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"<div class="mw-parser-output"><p>License: <a rel="nofollow" class="external text" href="https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/">Creative Commons<\/a><br>
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<\/p><\/div>"} Plot your points on the coordinate system, using the values you got from solving your three equations. In the example above, your graph would look like this. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/f2\/Do-Linear-Functions-Step-3Bullet1-Version-2.jpg\/v4-460px-Do-Linear-Functions-Step-3Bullet1-Version-2.jpg","bigUrl":"\/images\/thumb\/f\/f2\/Do-Linear-Functions-Step-3Bullet1-Version-2.jpg\/aid4531126-v4-728px-Do-Linear-Functions-Step-3Bullet1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"<div class="mw-parser-output"><p>License: <a rel="nofollow" class="external text" href="https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/">Creative Commons<\/a><br>
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<\/p><\/div>"} For any two points, there is only one way to connect them with a straight line. Use a ruler to join them with a straight line. Note that if you graph three points, and they don't all lie on the same line, then you've made a mistake somewhere. Go back and calculate again. In the example above, your graph would look like this. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/25\/Do-Linear-Functions-Step-4Bullet1-Version-2.jpg\/v4-460px-Do-Linear-Functions-Step-4Bullet1-Version-2.jpg","bigUrl":"\/images\/thumb\/2\/25\/Do-Linear-Functions-Step-4Bullet1-Version-2.jpg\/aid4531126-v4-728px-Do-Linear-Functions-Step-4Bullet1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"<div class="mw-parser-output"><p>License: <a rel="nofollow" class="external text" href="https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/">Creative Commons<\/a><br>
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