# 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) $x+2 y=6$"

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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 $y=-x+2$.

Updated on 10-Oct-2022 13:40:07