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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.