Question

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.

Answer 1

$2x+y=6\Rightarrow y=6-2xIfx=0,theny=6-2\times 0=6-0=6Ifx=2,theny=6-2\times 2=6-4=2$

$\begin{array}{ccc}x& 0& 2\\ y& 6& 2\end{array}$

Plot the points (0, 6) and (2, 2) on the graph and join them to get a line which intersects x=axis at (3, 0) and y-axis at (0, 6)

Now, co-ordinates of vertices of the shaded portion are (6, 0) (0, 0) and (3, 0).

Area of the shaded region =$\frac{1}{2}OA\times OB=\frac{1}{2}\times 3\times 6=9sq.units$