# Inequalities

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To graph inequalities of the form y <= b/a * x + c/a a line of the form

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


and an inequality of this line have to be created.

In case a = 0, that is if the equation of the line is bx + c = 0, the area of the inequality bx + c <= 0 is shown.

If one wants to show "greater than", inverse:true has to be used:

line = b.create('line', [c, b, a]);
ineq = b.create('inequality', [line], {inverse:true}),


In the following example, two lines are shown. The first, black line has the equation y = c or 0 = -1y + 0x + c, the second, blue line has the equation y = 2/3 x + 1 or 0 = -3y + 2x +1.

### The JavaScript code

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]]),
line1 = b.create('line', [function() { return [c.Value(), 0, -1]; }], {strokeColor: 'black'}),
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'});


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

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


If one wants to show "greater than" i.e. "ax + by + c >= 0" , inverse:true has to be used:

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

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