Построить линию заданную уравнением 2|x-1|+3|y-2|=6

Решите задачу:

$2|x-1|+3|y-2|=6, \\ x-1=0, \ x=1, \\ y-2=0, \\ y=2, \\ 1) \ x\ \textless \ 1, \ y\ \textless \ 2; \\ 2(1-x)+3(2-y)=6, \\ 2-2x+6-3y=6, \\ -2x-3y+2=0; \\ \begin{array}{c|cc}x&-2&4\\y=-\frac{2}{3}x+\frac{2}{3}&2&-2\end{array} \\ 2) \ x\ \textless \ 1, \ y\ \textgreater \ 2; \\ 2(1-x)+3(y-2)=6, \\ 2-2x+3y-6=6, \\ -2x+3y-10=0, \\ \begin{array}{c|cc}x&-2&1\\y=\frac{2}{3}x+\frac{10}{3}&2&4\end{array} \\ 3) \ x\ \textgreater \ 1, \ y\ \textgreater \ 2; \\ 2(x-1)+3(y-2)=6, \\ 2x-2+3y-6=6, \\ 2x+3y-14=0, \\ \begin{array}{c|cc}x&-2&1\\y=-\frac{2}{3}x+\frac{14}{3}&6&4\end{array}$
$4) \ x\ \textgreater \ 1, \ y\ \textless \ 2; \\ 2(x-1)+3(2-y)=6, \\2x-2+6-3y=6, \\ 2x-3y-2=0, \\ \begin{array}{c|cc}x&-2&4\\y=\frac{2}{3}x-\frac{2}{3}&-2&2\end{array}$