Three points (x₁, y₁), (x₂, y₂), and (x₃, y₃) are collinear (lie on the same line) if and only if

Therefore, with the points (-1, 1), (2, 2), and (6, 5) – we have (expanding on the first row)

Because the value of this determinant is not zero, the three points do not lie on the same line (not collinear).