The line of reflection has to be perpendicular bisector of the line AA'.
The slope of AA' is (18-12)/(7-3)=6/4=3/2
The slope of line M= -2/3
The midpoint of |AA'| is (5,15)
The equation of line M: 15=-2/3 x 5 +b
15= -10/3 +b
18 1/3=b
y=(-2/3)x+18 1/3 (in slope, y-intercept form)
or 2x+3y=55