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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 $y=-x+2$.