e39465ad2f
new file: Files/flashplayer_32_sa.exe
new file: favicon.ico
new file: globe.gif
new file: imgs/download.png
new file: imgs/zuck.jpg
new file: index.html
new file: other.ico
new file: script.js
new file: site.webmanifest
new file: sitemap.html
new file: styles/backround.css
new file: styles/border.css
new file: styles/fonts/Titillium_Web/OFL.txt
new file: styles/fonts/Titillium_Web/TitilliumWeb-Black.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Bold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-BoldItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLight.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Italic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Light.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-LightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Regular.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBoldItalic.ttf
new file: styles/fonts/webfontkit-20221027-163353/generator_config.txt
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-demo.html
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff2
new file: styles/fonts/webfontkit-20221027-165950/generator_config.txt
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-demo.html
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff2
new file: styles/style.css
new file: tools/2048/.gitignore
new file: tools/2048/.jshintrc
new file: tools/2048/CONTRIBUTING.md
new file: tools/2048/LICENSE.txt
new file: tools/2048/README.md
new file: tools/2048/Rakefile
new file: tools/2048/favicon.ico
new file: tools/2048/index.html
new file: tools/2048/js/animframe_polyfill.js
new file: tools/2048/js/application.js
new file: tools/2048/js/bind_polyfill.js
new file: tools/2048/js/classlist_polyfill.js
new file: tools/2048/js/game_manager.js
new file: tools/2048/js/grid.js
new file: tools/2048/js/html_actuator.js
new file: tools/2048/js/keyboard_input_manager.js
new file: tools/2048/js/local_storage_manager.js
new file: tools/2048/js/tile.js
new file: tools/2048/meta/apple-touch-icon.png
new file: tools/webretro/cores/neocd_libretro.js
new file: tools/webretro/cores/neocd_libretro.wasm
new file: tools/webretro/cores/nestopia_libretro.js
new file: tools/webretro/cores/nestopia_libretro.wasm
new file: tools/webretro/cores/o2em_libretro.js
new file: tools/webretro/cores/o2em_libretro.wasm
new file: tools/webretro/cores/opera_libretro.js
new file: tools/webretro/cores/opera_libretro.wasm
155 lines
7.9 KiB
HTML
155 lines
7.9 KiB
HTML
<!doctype html>
|
|
<html lang="en"><!-- #BeginTemplate "/Templates/Advanced.dwt" --><!-- DW6 -->
|
|
|
|
<!-- Mirrored from www.mathsisfun.com/algebra/graphing-linear-inequalities.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 01:02:29 GMT -->
|
|
<head>
|
|
<!-- #BeginEditable "doctitle" -->
|
|
<title>Graphing Linear Inequalities</title>
|
|
<meta name="description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents." />
|
|
<!-- #EndEditable -->
|
|
<meta name="keywords" content="math, maths, mathematics, school, homework, education" />
|
|
<meta http-equiv="content-type" content="text/html; charset=utf-8" />
|
|
<meta name="viewport" content="width=device-width; initial-scale=1.0; user-scalable=true;" />
|
|
<meta name="HandheldFriendly" content="true"/>
|
|
<meta http-equiv="pics-label" content='(PICS-1.1 "http://www.classify.org/safesurf/" L gen true for "http://www.mathsisfun.com" r (SS~~000 1))' />
|
|
<link rel="stylesheet" type="text/css" href="../style3.css" />
|
|
<script src="../main3.js" type="text/javascript"></script>
|
|
</head>
|
|
|
|
<body id="bodybg" class="adv">
|
|
<div class="bg">
|
|
<div id="stt"></div>
|
|
<div id="hdr"></div>
|
|
<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun" /></a></div>
|
|
<div id="advText">Advanced</div>
|
|
<div id="gtran"><script type="text/javascript">document.write(getTrans());</script></div>
|
|
<div id="gplus"><script type="text/javascript">document.write(getGPlus());</script></div>
|
|
<div id="adTopOuter" class="centerfull noprint">
|
|
<div id="adTop">
|
|
<script type="text/javascript">document.write(getAdTop());</script>
|
|
</div>
|
|
</div>
|
|
<div id="adHide">
|
|
<div id="showAds1"><a href="javascript:showAds()">Show Ads</a></div>
|
|
<div id="hideAds1"><a href="javascript:hideAds()">Hide Ads</a><br>
|
|
<a href="../about-ads.html">About Ads</a></div>
|
|
</div>
|
|
<div id="menuWide" class="menu">
|
|
<script type="text/javascript">document.write(getMenu(0));</script>
|
|
</div>
|
|
<div id="linkto">
|
|
<div id="linktort"><script type="text/javascript">document.write(getLinks());</script></div>
|
|
</div>
|
|
<div id="search" role="search"><script type="text/javascript">document.write(getSearch());</script></div>
|
|
<div id="menuSlim" class="menu">
|
|
<script type="text/javascript">document.write(getMenu(1));</script>
|
|
</div>
|
|
<div id="menuTiny" class="menu">
|
|
<script type="text/javascript">document.write(getMenu(2));</script>
|
|
</div>
|
|
<div id="extra"></div>
|
|
</div>
|
|
<div id="content" role="main"><!-- #BeginEditable "Body" -->
|
|
<h1 class="center">Graphing Linear Inequalities</h1>
|
|
<p>This is a graph of a linear <a href="inequality.html">inequality</a>:</p>
|
|
<p class="center"><img src="images/linear-inequality-x-2.svg" alt="linear inequality y <= x +2" /><br />
|
|
<span class="larger">The inequality y ≤ x + 2</span></p>
|
|
<p>You can see the <span class="larger">y = x + 2</span> line, and the shaded area is where y is less than or equal to <span class="larger"> x + 2</span></p>
|
|
|
|
<div class="def">
|
|
<h3>Linear Inequality</h3>
|
|
<p>A Linear Inequality is like a <a href="linear-equations.html">Linear Equation</a> (such as <b>y = 2x+1</b>) ...</p>
|
|
<p class="center"> ... but it will have an <a href="inequality-solving.html">Inequality</a> like <b><, >, ≤, or ≥</b> instead of an <b>=</b>.</p>
|
|
</div>
|
|
<h2>How to Graph a Linear Inequality</h2>
|
|
<p>First, graph the "equals" line, then shade in the correct area.</p>
|
|
<p>There are three steps:</p>
|
|
<ul class="bigul">
|
|
<li>Rearrange the equation so "y" is on the left and everything else on the right.</li>
|
|
<li>Plot the "<b>y=</b>" line (make it a solid line for <b>y≤</b> or <b>y≥</b>, and a dashed line for <b>y<</b> or <b>y></b>)</li>
|
|
<li>Shade above the line for a "greater than" (<b>y></b> or <b>y≥</b>) <br />
|
|
or below the line for a "less than" (<b>y<</b> or <b>y≤</b>).</li>
|
|
</ul>
|
|
<p>Let us try some examples: </p>
|
|
<div class="example">
|
|
<h3>Example: y≤2x-1</h3>
|
|
<p>1. The inequality already has "y" on the left and everything else on the right, so no need to rearrange</p>
|
|
<p>2. Plot <b>y=2x-1</b> (as a solid line because y≤ includes <b>equal to</b>)</p>
|
|
<p class="center"><img src="images/linear-inequality-2xm1a.svg" alt="y = 2x -1" /></p>
|
|
<p>3. Shade the area below (because y is <b>less than</b> or equal to)</p>
|
|
<p class="center"><img src="images/linear-inequality-2xm1b.svg" alt="linear inequality y <= 2x -1 shaded" /></p>
|
|
</div>
|
|
<div class="example">
|
|
<h3>Example: 2y − x ≤ 6</h3>
|
|
<p>1. We will need to rearrange this one so "y" is on its own on the left:</p>
|
|
<div class="so">Start with: 2y − x ≤ 6</div>
|
|
<div class="so">Add x to both sides: 2y ≤ x + 6</div>
|
|
<div class="so">Divide all by 2: y ≤ x/2 + 3</div>
|
|
<p> </p>
|
|
<p>2. Now plot <b>y = x/2 + 3</b> (as a solid line because y≤ includes <b>equal to</b>)</p>
|
|
<p class="center"><img src="images/linear-inequality-x2p3a.svg" alt="y = x/2 + 3" /></p>
|
|
<p>3. Shade the area below (because y is <b>less than</b> or equal to)</p>
|
|
<p class="center"><img src="images/linear-inequality-x2p3b.svg" alt="linear inequality y <= x/2 + 3 shaded" /></p>
|
|
</div>
|
|
|
|
<div class="example">
|
|
<h3>Example: y/2 + 2 > x</h3>
|
|
<p>1. We will need to rearrange this one so "y" is on its own on the left:</p>
|
|
<div class="so">Start with: y/2 + 2 > x</div>
|
|
<div class="so">Subtract 2 from both sides: y/2 > x − 2</div>
|
|
<div class="so">Multiply all by 2: y > 2x − 4</div>
|
|
<p> </p>
|
|
<p>2. Now plot <b>y = 2x − 4</b> (as a dashed line because y> does not include equals to)</p>
|
|
<p class="center"><img src="images/linear-inequality-2xm4a.svg" alt="y = 2x - 4" /></p>
|
|
<p>3. Shade the area above (because y is <b>greater than</b>)</p>
|
|
<p class="center"><img src="images/linear-inequality-2xm4b.svg" alt="linear inequality y > 2x - 4 " /></p>
|
|
</div>
|
|
<p>The dashed line shows that the inequality does <b>not</b> include the line <b>y=2x-4</b>.</p>
|
|
<p> </p>
|
|
<h2>Two Special Cases</h2>
|
|
<p>You could also have a horizontal or vertical line:</p>
|
|
<table border="0">
|
|
<tr>
|
|
<td align="center"><img src="images/linear-inequality-ylt4.svg" alt="linear inequality y<4" /></td>
|
|
<td align="center"><img src="images/linear-inequality-xgt1.svg" alt="linear inequality x>=1" /></td>
|
|
</tr>
|
|
<tr>
|
|
<td align="center">This shows where y is less than 4 <br />
|
|
(from, but not including, the line <b>y=4</b> on down)<br />
|
|
Notice that we have a dashed line to show that it does not include where y=4</td>
|
|
<td align="center">This one doesn't even have y in it!<br />
|
|
It has the line <b>x=1</b>, and is shaded for all values of x greater than (or equal to) 1</td>
|
|
</tr>
|
|
</table>
|
|
<p>
|
|
</p>
|
|
<div class="questions">
|
|
|
|
<script type="text/javascript">getQ(7426, 7427, 7428, 7429, 7430, 7431, 7432, 7433, 7434, 7435);</script>
|
|
|
|
</div>
|
|
|
|
<div class="related">
|
|
<a href="../data/inequality-grapher.html">Inequality Grapher</a>
|
|
<a href="inequality.html">Inequalities</a>
|
|
<a href="inequality-solving.html">Solving Inequalities</a>
|
|
<a href="inequality-questions-solving.html">Solving Inequality Word Questions</a>
|
|
<a href="index.html">Algebra Index</a>
|
|
</div>
|
|
<!-- #EndEditable --></div>
|
|
<div id="adend" class="centerfull noprint">
|
|
<script type="text/javascript">document.write(getAdEnd());</script>
|
|
</div>
|
|
<div id="footer" class="centerfull noprint">
|
|
<script type="text/javascript">document.write(getFooter());</script>
|
|
</div>
|
|
<div id="copyrt">
|
|
Copyright © 2017 MathsIsFun.com
|
|
</div>
|
|
|
|
<script type="text/javascript">document.write(getBodyEnd());</script>
|
|
</body>
|
|
<!-- #EndTemplate -->
|
|
<!-- Mirrored from www.mathsisfun.com/algebra/graphing-linear-inequalities.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 01:02:31 GMT -->
|
|
</html>
|