this is all complicated to me, as I simply take on equation \(y=\frac{1}{2}x-1 \)
\(x=\frac{1}{2}x-1 \), \(x/2=-1 \), \(x=-2 \) and \(y=\frac{1}{2}*(-2)-1=-2 \). Answer is (-2, -2) and it's A.

We want to find a point on the graph where the x-coordinate equals the y-coordinate.
In other words, we want: \(x = y\)

So, let's replace \(y\) with \(x\) in the original equation to get: \(x=\frac{1}{2}x-1 \)

Subtract \(\frac{1}{2}x\) from both sides of the equation to get: \(\frac{1}{2}x=-1 \)

Multiply both sides of the equation by \(2\) to get: \(x=-2\)

So, when \(x=-2\), x- and y-coordinates are equal.

Answer: A