Draw the graph of the equation $2x + y = 6$. Shade the region bounded by the graph and the coordinate axes. Also find the area of the shaded region.

Given:

Given equation is $2x + y = 6$.

To do:

We have to draw the graph and find the area of the shaded region bounded by the graph and the coordinate axes.

Solution:

To represent the above equation graphically we need at least two solutions for the given equation.

For equation $2x + y = 6$  

$y=6-2x$

If $x=0$, then

$y=6-2(0)$

$=6-0$

$=6$

If $x=3$, then

$y=6-2(3)$

$=6-6$

$=0$

$x$	$0$	$3$
$y$	$6$	$0$

Plot the points $A(0, 6)$ and $B(3, 0)$ on the graph and join them to get the graph of the given equation.

The above situation can be plotted graphically as below:

The coordinates of the points where the graph cuts the coordinates axes are $(0,6)$ and $(3,0)$. 

 Area of a triangle$=\frac{1}{2}bh$

In the graph, the height of the triangle is the distance between point A and x-axis.

Height of the triangle$=6$ units.

Base of the triangle$=$Distance between the points A and y-axis.

Base of the triangle$=3$ units.

Area of the shaded region $=\frac{1}{2}\times6\times3$

$=9$ sq. units.