Answer: The correct option is
(B) [tex]\left(\frac{1}{2},1\right).[/tex]
Step-by-step explanation: We are given to select the point that does not lie on the graph of the following line :
[tex]y=2x-2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Any point that does not lie on the graph of (i) will not satisfy the equation.
If [tex](x, y)=\left(-\frac{1}{2},-3\right),[/tex] then
[tex]R.H.S.=2x-2=2\times \left(-\dfrac{1}{2}\right)-2=-1-2=-3=y=L.H.S.[/tex]
So, this option is NOT correct.
If [tex](x, y)=\left(\frac{1}{2},1\right),[/tex] then
[tex]R.H.S.=2x-2=2\times \left(\dfrac{1}{2}\right)-2=1-2=-1\neq y=L.H.S.[/tex]
So, this option is correct.
If [tex](x, y)=(-1,-4),[/tex] then
[tex]R.H.S.=2x-2=2\times (-1)-2=-2-2=-4=y=L.H.S.[/tex]
So, this option is NOT correct.
Thus, the correct option is (B).
