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

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We need to find the point with equal coordinates on the line y= 0.5x -0.5.

The point can be expressed as (m, m).

Now, as this lies on the line y= 0.5x -0.5 , we have

m = 0.5*m - 0.5

subtract 0.5*m from both the sides

=> 0.5m = -0.5

divide by 0.5

=> m = -1

The point has equal coordinates (-1,-1) and 0.5*-1 - 0.5 = -1

**Therefore we have the point (-1,-1) on the line y= 0.5x -0.5. **

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**

The given line is y = 0.5x-0.5.

Since both x and y coordinates are equal and is a point on the line y = 0.5x-0.5, we assume that ( c , c ) is point.

Therefore (c,c) should satisfy y = 0.5x-0.5.

So we substitute y=c and x = c in y = 0.5x-0.5:

c = 0.5c -0.5.

c-0.5c = -0.5.

0.5c = -0.5.

Therefore c = -0.5/0.5 = -1.

Therefore (-1, -1) is a point on the line y = 0.5x-0.5