Draw the graph of each of the following linear equations in two variables:<br/><br/>(i) $x+y=4$ <br/><br/>(ii) $x-y=2$ <br/><br/>(iii) $y=3 x$ <br/><br/>(iv) $3=2 x+y$

Solution:

(i) $x+y=4$

It can be observed that $x=0, y=4$ and $x=4, y=0$ are solutions of the above equation. Therefore, the solution table is as follows.



The graph of this equation is constructed as follows.



(ii) $x-y=2$

It can be observed that $x=4, y=2$ and $x=2, y=0$ are solutions of the above equation. Therefore, the solution table is as follows.



The graph of the above equation is constructed as follows.



(iii) $y=3 x$

It can be observed that $x=-1, y=-3$ and $x=1, y=3$ are solutions of the above equation. Therefore, the solution table is as follows.



The graph of the above equation is constructed as follows.



(iv) $3=2 x+y$

It can be observed that $x=0, y=3$ and $x=1, y=1$ are solutions of the above equation. Therefore, the solution table is as follows.



The graph of this equation is constructed as follows.