web2.0calc.com question

To emphasize what Melody did:

The equation:  |3x| + |4y|  =  12

Can be split into 4 separate equations; 2 for the  |3x| = ± 3x  and  2 for the  |4y| = ± 4y :

--->                 3x + 4y  =  12       --->   y  =  (12 - 3x)/4

                      -3x + 4y  =  12       --->   y  =  (12 + 3x)/4

                       3x - 4y  =  12       --->   y  =  (12 - 3x)/-4

                      -3x - 4y  =  12        --->   y  =  (12 + 3x)/-4  

Graphing these individually will give you the parallelogram that Melody got.

I 'cheated' a bit because I ran off and graphed it.

Here is the graph.

https://www.desmos.com/calculator/rrxgm9spsh

I expected it to be a parallelogram and it was.

(I can talk more about this if you want me too)

The easiest way to find the area is to split it into 2 congruent trianges

base = 8 units and height = 3 units

Area =    $${\mathtt{2}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{3}}\right) = {\mathtt{24}}$$    units squared. 

Note the graph.......https://www.desmos.com/calculator/dbrn6oivcb

These are two triangles which have a base = 8 and a height  = 3

So, the area is just 2(1/2)(8)(3)  = 24 units

Melody and I both cheated...(but she cheated first.....and as chief mod, she should set a BETTER EXAMPLE to the people of Camelot!!!)...LOL!!!!

Thanks Geno. :)