# Inequalities

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
```