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We'll denote the point with that has equal coordinates as M(m,m).
Since the point is located on the line y = 0.5x - 0.5, it's coordinates verify the expression of the line.
We'll put y = f(x) and we'll substitute x and y by the coordinates of the given point:
f(m) = 0.5m - 0.5 (1)
But f(m) = m (2)
We'll conclude from (1) and (2) that:
0.5m - 0.5 = m
We'll isolate m to the left side.
0.5m - m = 0.5
-0.5m = 0.5
We'll divide by -0.5 both sides:
m = -1
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