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.