Question

If a linear equation has solutions $(2,-2),(0,0)$ and $(-2,2)$, then it is of the form

• A. $y-x=0$
• B. $x+y=0$
• C. $2x+y=0$
• D. $x+2y=0$

Answer 1

The correct option is B $x+y=0$

Let the linear equation be $y=ax+b$ ...(1)
By substituting $(x,y)=(0,0)$ in the equation, we get,
$0=0x+b\Rightarrow b=0$
Now, our equation becomes $y=ax$ (Since $b=0$) ...(2)
By substituting $(x,y)=(2,-2)$ in the equation, we get
$-2=2a\Rightarrow a=-1$
$\therefore$ Final equation becomes
$y=-x$ or $x+y=0$
Hence, option B.