the are of the triangle formed by 2x+3y=6 and the coordinate axes is

given equation is=2x+3y=6---(1)

 we rewrite the equation ,=3y=-2x+6

                                        y=-(2/3)x+2  

in these equation,slope=-2/3

the coordinating point here is  (o,2)  

set y=0 then  ,0=-(2/3)x+2

                       2/3x=2

                           x=3

here the coordinating point is,(3,0)

using this coordinate we draw one graph,then

from the graph height will be come,2

and length will be come,3

area =2*3/2=3

By rearranging the equation for y you can plot the graph on paper.

The equation you get is y=(6-2x)/3. The area sectioned off by the y-axis, x-axis and the linear line itself is the triangle.

The points for this triangle are (0,0) (0,2) (3,0).  The area is (2x3)/2, which is 3, because of the equation 1/2 * base * height. The height is the size of y and the length the size of the x.

Hopes this helps. :) 

SOL--- The equation of given line is 2x + 3y =6 . let the given line intersect x axis at point A( x ,0 ) , and Y axis at point B (O,y) . By putting  the coordinates of point in given equation we get , x =3 , ie coordinate s of point A ( 3,0 ) , similarly coordinate of point B is (0,2) hence we got the triangle with sides 2 and 3 .therefore area of triangle is 3 squnits