Three points A (2; -3) B (-4; 1) C (1; -1) are given. Do these points lie on the same straight line?

You can always draw a straight line through 2 points. Let the straight line pass through points A and C. Then we find the equation of this straight line: In general: y = kx + b Substitute the coordinates of point A: -3 = 2k + b Substitute the coordinates of point C: -1 = k + b The system of equations is obtained, of which k = -2, b = 1. Hence, the equation of the straight line passing through points A and C y = -2x + 1. Let’s check if the point B belongs to the given line: y = -2 * (- 4) +1, y = 9. But at point B = 1 => point B does not belong to this straight line => points do not lie on one straight line.
Answer: do not lie.