Difference between revisions of "Inequalities"

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To graph inequalities of the form  
+
To graph inequalities of the "less than" form
''y <= b/a * x + c/a''
+
"ax + by + c <= 0"
a line of the form
 
 
<source lang="javascript">
 
<source lang="javascript">
line = b.create('line', [c, b, a]);
+
var line = board.create('line', [c, b, a]),
ineq = b.create('inequality', [line]),
+
ineq = board.create('inequality', [line]);
 
</source>
 
</source>
and an equality of this line have to be created.
+
 
If one wants to show "greater than", ''inverse:true'' has to be used:
+
If one wants to show "greater than" i.e.  "ax + by + c >= 0" , ''inverse:true'' has to be used:
 
<source lang="javascript">
 
<source lang="javascript">
line = b.create('line', [c, b, a]);
+
var line = board.create('line', [c, b, a]),
ineq = b.create('inequality', [line], {inverse:true}),
+
ineq = board.create('inequality', [line], {inverse:true});
 
</source>
 
</source>
  
 
In the following example, two lines are shown.
 
In the following example, two lines are shown.
The first, black line has the equation ''y = c'' or ''0 = -1y + 0x + c'',
+
The first, blue line has the equation "y = 2x + 3" or "2x - 1y + 3 = 0",
the second, blue line has the equation ''y = 2/3 x + 1'' or ''0 = -3y + 2x +1''.
+
the second, black line has the equation "x = 3" or "1x + 0y - 3 = 0".
  
In case ''a = 0'', that is if the equation of the line is ''bx + c = 0'', the area of the inequality
+
For these equations, the inequalities plotted are
''bx + c <= 0'' is shown.
+
"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.
  
 
<jsxgraph width="400" height="400" box="box1">
 
<jsxgraph width="400" height="400" box="box1">
 
(function() {
 
(function() {
var b = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 5, 5, -5], axis:true});
+
    var b = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 5, 5, -5], axis:true});
var c = b.create('slider', [[-3,4], [2,4], [-5,1,5]]),
+
    var line1 = b.create('line', [3, 2, -1]), // Line y = 2x + 3 or 2x - 1y + 3 = 0
    line1 = b.create('line', [function() { return [c.Value(), 0, -1]; }], {strokeColor: 'black'}),
+
     ineq1 = b.create('inequality', [line1], {fillColor: 'yellow'});  //This would plot the inequality 2x - y + 3 <= 0
     ineq1 = b.create('inequality', [line1], {inverse: true}),
 
  
     line2 = b.create('line', [1, 2, -3])// Line y = 2/3 x + 1 or 0 = -3y + 2x +1
+
     var line2 = b.create('line', [-3, 1, 0], {strokeColor: 'black'}); // Line x = 3 or 1x + 0y - 3 = 0
     ineq2 = b.create('inequality', [line2], {fillColor: 'yellow'});
+
     var ineq2 = b.create('inequality', [line2], {inverse: true, fillColor: 'red'}); //This would plot the inequality 1x + 0y - 3 >= 01x + 0y - 3 >= 0
  
 
})();
 
})();
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===The JavaScript code===
 
===The JavaScript code===
 
<source lang="javascript">
 
<source lang="javascript">
var b = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 5, 5, -5], axis:true});
+
    var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 5, 5, -5], axis:true});
var c = b.create('slider', [[-3,4], [2,4], [-5,1,5]]),
+
    var line1 = board.create('line', [3, 2, -1]), // Line y = 2x + 3 or 2x - 1y + 3 = 0
    line1 = b.create('line', [function() { return [c.Value(), 0, -1]; }], {strokeColor: 'black'}),
+
     ineq1 = board.create('inequality', [line1], {fillColor: 'yellow'}); //This would plot the inequality 2x - y + 3 <= 0
    ineq1 = b.create('inequality', [line1], {inverse: true}),
 
 
 
    line2 = b.create('line', [1, 2, -3]), // Line y = 2/3 x + 1 or 0 = -3y + 2x +1
 
     ineq2 = b.create('inequality', [line2], {fillColor: 'yellow'});
 
  
 +
    var line2 = board.create('line', [-3, 1, 0], {strokeColor: 'black'}); // Line x = 3 or 1x + 0y - 3 = 0
 +
    var ineq2 = board.create('inequality', [line2], {inverse: true, fillColor: 'red'});  //This would plot the inequality 1x + 0y - 3 >= 0
 
</source>
 
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Calculus]]
 
[[Category:Calculus]]

Latest revision as of 11:57, 8 June 2017

To graph inequalities of the "less than" form "ax + by + c <= 0"

var line = board.create('line', [c, b, a]),
ineq = board.create('inequality', [line]);

If one wants to show "greater than" i.e. "ax + by + c >= 0" , inverse:true has to 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 first, blue line has the equation "y = 2x + 3" or "2x - 1y + 3 = 0", the second, 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.

The JavaScript code

    var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-5, 5, 5, -5], axis:true});
    var line1 = board.create('line', [3, 2, -1]), // Line y = 2x + 3 or 2x - 1y + 3 = 0
    ineq1 = board.create('inequality', [line1], {fillColor: 'yellow'});  //This would plot the inequality 2x - y + 3 <= 0

    var line2 = board.create('line', [-3, 1, 0], {strokeColor: 'black'}); // Line x = 3 or 1x + 0y - 3 = 0
    var ineq2 = board.create('inequality', [line2], {inverse: true, fillColor: 'red'});  //This would plot the inequality 1x + 0y - 3 >= 0