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Inequalities (half-planes)
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<iframe 
    src="https://www.jsxgraph.org/share/iframe/inequalities-half-planes" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Inequalities (half-planes)" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution 4.0 International License.
    https://creativecommons.org/licenses/by/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    const board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-5, 5, 5, -5],
        axis: true
    });
    
    // Line y = 2x + 3 or 
    // 2x - 1y + 3 = 0
    var line1 = board.create('line', [3, 2, -1]); 
    
    // Plot the area 2x - y + 3 <= 0
    var ineq1 = board.create('inequality', [line1], {fillColor: 'yellow'}); 
    
    // Vertical line x = 3 or 
    // 1x + 0y - 3 = 0
    var line2 = board.create('line', [-3, 1, 0], {strokeColor: 'black'}); 
    
    // Plot the area 1x + 0y - 3 >= 0
    var ineq2 = board.create('inequality', [line2], {inverse: true, fillColor: 'red'}); 
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    axis: true
});

// Line y = 2x + 3 or 
// 2x - 1y + 3 = 0
var line1 = board.create('line', [3, 2, -1]); 

// Plot the area 2x - y + 3 <= 0
var ineq1 = board.create('inequality', [line1], {fillColor: 'yellow'}); 

// Vertical line x = 3 or 
// 1x + 0y - 3 = 0
var line2 = board.create('line', [-3, 1, 0], {strokeColor: 'black'}); 

// Plot the area 1x + 0y - 3 >= 0
var ineq2 = board.create('inequality', [line2], {inverse: true, fillColor: 'red'}); 
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Inequalities (half-planes)" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution 4.0 International License.
   https://creativecommons.org/licenses/by/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-5, 5, 5, -5],
       axis: true
   });
   
   // Line y = 2x + 3 or 
   // 2x - 1y + 3 = 0
   var line1 = board.create('line', [3, 2, -1]); 
   
   // Plot the area 2x - y + 3 <= 0
   var ineq1 = board.create('inequality', [line1], {fillColor: 'yellow'}); 
   
   // Vertical line x = 3 or 
   // 1x + 0y - 3 = 0
   var line2 = board.create('line', [-3, 1, 0], {strokeColor: 'black'}); 
   
   // Plot the area 1x + 0y - 3 >= 0
   var ineq2 = board.create('inequality', [line2], {inverse: true, fillColor: 'red'}); 
</jsxgraph>

Inequalities (half-planes)

Analytic
Geometry
To graph a *half-plane* write the separating line in the form `ax + by + c = 0` and construct it with ``` var line = board.create('line', [c, b, a]), ``` Then, ``` ineq = board.create('inequality', [line]); ``` shows the points `(x,y)` with `ax + by + c <= 0`. If one wants to show *greater than*, i.e. plot the points `(x,y)` with `ax + by + c >= 0` , the attribute `inverse:true` can be used: ``` var line = board.create('line', [c, b, a]), ineq = board.create('inequality', [line], {inverse:true}); ``` In the following example, two lines are shown. - The blue line has the equation `y = 2x + 3` or `2x - 1y + 3 = 0`, - the black line has the equation `x = 3` or `1x + 0y - 3 = 0`. For these equations, the inequalities plotted are - `2x - y + 3 <= 0` (less than form hence don't add `inverse: true`) - yellow region and - `1x + 0y - 3 >= 0` (greater than form hence do add "inverse: true") - red region.
Have also a look at the examples 
// Define the id of your board in BOARDID

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    axis: true
});

// Line y = 2x + 3 or 
// 2x - 1y + 3 = 0
var line1 = board.create('line', [3, 2, -1]); 

// Plot the area 2x - y + 3 <= 0
var ineq1 = board.create('inequality', [line1], {fillColor: 'yellow'}); 

// Vertical line x = 3 or 
// 1x + 0y - 3 = 0
var line2 = board.create('line', [-3, 1, 0], {strokeColor: 'black'}); 

// Plot the area 1x + 0y - 3 >= 0
var ineq2 = board.create('inequality', [line2], {inverse: true, fillColor: 'red'});

license

This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.