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Draw the graph of the equation $\frac{x}{3} + \frac{y}{4} = 1$. Also find the area of the triangle formed by the line and the co-ordinate axes.
Given:
Given equation is $\frac{x}{3} + \frac{y}{4} = 1$.
To do:
We have to draw the graph and find the area of the triangle formed by the line and the co-ordinate axes.
Solution:
To represent the above equation graphically we need at least two solutions for the given equation.
$\frac{x}{3}+\frac{y}{4}=1$
$4 x+3 y=12$
$4 x=12-3 y$
$x=\frac{12-3 y}{4}$
If $y=0$, then $x=\frac{12-3 \times 0}{4}$
$=\frac{12-0}{4}$
$=\frac{12}{4}$
$=3$
If $y=4$, then
$x=\frac{12-3 \times 4}{4}$
$=\frac{12-12}{4}$
$=\frac{0}{4}$
$=0$
$x$ | $3$ | $0$ |
$y$ | $0$ | $4$ |
Plot the points $A(3, 0)$ and $B(0, 4)$ 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 $(0,4)$ and $(3,0)$.
Area of a triangle$=\frac{1}{2}bh$In the graph, the height of the triangle is the distance between point B and x-axis.
Height of the triangle$=4$ units.
Base of the triangle$=$Distance between the points A and y-axis.Base of the triangle$=3$ units.
Area of the shaded region $=\frac{1}{2}\times4\times3$
$=6$ sq. units.