I am having some trouble understanding how to determine the parametric equation of a line segment between A(1,1) and B(-1,1).
I did some research and came across the following relation:
$$x(t)=(1-t)\times 1+t\times (-1)=-2t+1$$ $$y(t)=(1-t)\times1+t\times1=1$$
However they find $x(t)=-t$ and $y(t)=1$
What am I doing wrong with the x component ?
You are asking that $t \in [0,1]$ while they allow $t \in [-1,1]$. Given the proper range of $t$, you are both getting the same result. When the allowable range of the parameter is restricted you need to specify the range.
In this case, because $y$ is constant, any parameterization of $x$ that takes it over $[-1,1]$ is correct. If $y$ is not constant, you need to synchronize them. For example, if we wanted the segment from $(0,0)$ to $(3,4)$ we could say $x(t)=3t, y(t)=4t, t \in [0,1]$ or $x(t)=t, y(t)=\frac 43t, t \in [0,3]$