Draw the graphs of the equations $x-y+1=0$ and $3x+2y-12=0$. Determine the coordinates of the vertices of the triangle formed by these lines and the $x$-axis,and shade the triangular region.

(N/A) For the equation $x-y+1=0$,we can write $x=y-1$. The table of values is:

$x$	$0$	$1$	$2$
$y$	$1$	$2$	$3$

For the equation $3x+2y-12=0$,we can write $x=\frac{12-2y}{3}$. The table of values is:

$x$	$4$	$2$	$0$
$y$	$0$	$3$	$6$

By plotting these points on a graph,we obtain two intersecting lines. The lines intersect each other at the point $(2,3)$ and intersect the $x$-axis at $(-1,0)$ and $(4,0)$.
Thus,the vertices of the triangle formed by these lines and the $x$-axis are $(2,3)$,$(-1,0)$,and $(4,0)$.