From the choices given below, choose the equation whose graphs are given in Fig. $ 4.6 $ and Fig. 4.7.
For Fig. 4. 6

(i) $ y=x $
(ii) $ x+y=0 $
(iii) $ y=2 x $
(iv) $ 2+3 y=7 x $
For Fig. $ 4.7 $


(i) $ y=x+2 $
(ii) $ y=x-2 $
(iii) $ y=-x+2 $
(iv) $ x+2 y=6 $"

To do: 

We have to find the equations whose graphs are given in fig $4.6$ and fig $4.6$.

Solution:

For Fig $4.6$

Let us substitute the given points in each of the equations in the options.

The given points should satisfy the equation whose graph is given in the figure.

Therefore,

(i) $(-1, 1)$

$y=x$

$-1≠1$

(ii) $(-1, 1)$

$x+y=0$

$-1+1=0$

$0+0=0$

$1-1=0$

Therefore, $(-1, 1)$ and $(1, -1)$ satisfy the equation $x+y=0$.

(iii) $(-1, 1)$

$y=2x$

$1=2(-1)$

$1≠-2$

(iv) $(-1, 1)$

$2+3y=7x$

$2+3(1)=7(-1)$

$2+3=-7$

$5≠-7$

Hence, the equation whose graph is given in the figure $4.6$ is $x+y=0$. 

For Fig $4.7$

Let us substitute the given points in each of the equations in the options.

The given points should satisfy the equation whose graph is given in the figure.

Therefore,

(i) $(-1, 3)$

$y=x+2$

$3≠-1+2$

(ii) $(-1, 3)$

$y=x-2$

$3≠-1-2$

(iii) $(-1, 3)$

$y=-x+2$

$-x+2=-(-1)+2$

$=1+2$

$=3$

$(2, 0)$

$y=-x+2$

$-x+2=-2+2$

$=0$

$=y$

Therefore, $(-1, 3)$ and $(2, 0)$ satisfy the equation $y=-x+2$.

(iv) $(-1, 3)$

$x+2y=6$

$x+2y=-1+2(3)$

$=-1+6$

$=5$

$≠6$

Hence, the equation whose graph is given in the figure $4.7$ is $y=-x+2$.