We are given with four linear equations and need to find the best option which shows the relationship between x and y in accordance with the given table . So , for this question as their are three ordered pairs , so it will be long to put all values of x and y in every equation . So , we will be checking only for one ordered pair, let's say be 2nd i.e (1,-2)
Checking for equation one :
[tex]{:\implies \quad \sf y=x+2}[/tex]
[tex]{:\implies \quad \sf -2=1+2}[/tex]
[tex]{:\implies \quad \sf -2=3}[/tex]
As , it's not possible . So this option is wrong
Checking for equation two :
[tex]{:\implies \quad \sf y=x-2}[/tex]
[tex]{:\implies \quad \sf -2=1-2}[/tex]
[tex]{:\implies \quad \sf -2=-1}[/tex]
As , it's not possible . So this option is wrong
Checking for equation three :
[tex]{:\implies \quad \sf y=2x}[/tex]
[tex]{:\implies \quad \sf -2=2\times 1}[/tex]
[tex]{:\implies \quad \sf -2=2}[/tex]
As , it's not possible . So this option is wrong
Checking for equation four :
[tex]{:\implies \quad \sf y=-2x}[/tex]
[tex]{:\implies \quad \sf -2=-2\times 1}[/tex]
[tex]{:\implies \quad \sf -2=-2}[/tex]
As the fourth equation satisfied the ordered pair ,
Hence , Option D) y = -2x is correct
