It is known that the intersection points a of the image of the first-order function y = MX + m-2 and y = 2x-3 are on the y-axis, and their intersection points with the x-axis are respectively point B and point C. (1) find the value of M and the area of △ ABC; (2) find the coordinates of the point on the image of the first-order function y = MX + m-2 whose distance to the x-axis is equal to 2

It is known that the intersection points a of the image of the first-order function y = MX + m-2 and y = 2x-3 are on the y-axis, and their intersection points with the x-axis are respectively point B and point C. (1) find the value of M and the area of △ ABC; (2) find the coordinates of the point on the image of the first-order function y = MX + m-2 whose distance to the x-axis is equal to 2

(1) Substituting x = 0 into y = 2x-3 to get y = - 3, so the coordinates of point a are (0, - 3), substituting y = 0 into y = 2x-3 to get 2x-3 = 0, and the solution is x = 32, so the coordinates of point C are (32, 0), substituting a (0, - 3) into y = MX + m-2 to get m-2 = - 3, and the solution is m = - 1; so the analytic formula of line AB is y = - x-3, substituting y = 0 into y = - x-3 to get