Determine the point with equal coordinates on the line yDetermine the point with equal coordinates on the line y=0.5x-0.5

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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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