find a relation between x and y if the points (x,y),(1,2),(7,0)are collinear

If given points are collinear then area of triangle formed by them must be zero.

Or, ½ [x₁(y₂ – y₃) + x₂ (y₃ – y₁) + x₃ (y₁ – y₂)] = 0

Or, ½ [x(2 – 0) + 1 (0 – y) + 7( y – 2)] = 0

Or, 2x – y + 7y – 14 = 0

Or, 2x + 6y – 14 = 0

Or, x + 3y – 7 = 0

The last equation gives the relation between x and y.