To find the distance between a point (x1,y1) and line L with equation y=m*x+b, where m is not 0.L:=x->m*x+b;<Text-field layout="Heading 1" style="Heading 1">1. One finds the line R perpendicular to L which passes through (x1,y1)</Text-field>The slope of any line perpendicular to L is -1/m if m is not zero. Hence the equation is y=(-1/m)*x+B, for some number B. Since The point (x1,y1) is in the line, y1=(-1/m)*x1+B. Therefore, B=y1+x1/m. The equation of the line perperndicular to L and passing through (x1,y1) isR:=x->(-1/m)*x+y1+x1/m;<Text-field layout="Heading 1" style="Heading 1">2. One finds the point (X,Y) of intersection between L and R</Text-field>Inter:=solve({L(X)=Y,R(X)=Y},{X,Y});assign(%);<Text-field layout="Heading 1" style="Heading 1">One finds the distance between (X,Y) and (X1,Y1). This is the distance we are looking for.</Text-field>d:=(m,b,x1,y1)->sqrt(( X-x1)^2+(Y-y1)^2);simplify(d(m,b,x1,y1));di:=(m,b,x1,y1)->abs(b-y1+m*x1)/sqrt(1+m^2);Now we consider the data,data := [[.583261688, 4.870738845], [10.34760496, 12.24799310], [6.818265100,
9.386049256], [-1.247008722, 5.648509794], [2.610788138, 6.687248645], [5.2027\
58576, 12.16682966], [-.198344401, 5.672376080], [-5.845268622, -.299527935],
[4.841758178, 11.58593557], [4.736340892, 13.46726732], [-8.377048078, -1.7960\
56022], [8.626478435, 13.38610384], [3.306593731, 10.69007144], [-7.283248994,
-5.071023470], [-6.325341028, .201251945], [4.661618855, 10.35882183], [6.5388\
34058, 10.37528223], [-3.707412732, 3.571559549], [-1.222404998, 1.763777954],
[-4.331621618, -3.043378658], [-5.696654642, .435640176], [-1.202230640, 5.348\
763305], [-.163907489, 4.231178940], [2.463893670, 8.318784687], [3.249933696,
10.44231960], [-6.033926206, -1.183760270], [7.545915316, 11.12980980], [-8.38\
5756736, -2.884912135], [3.892551676, 8.507218210], [-6.155724441, -2.79157060\
9], [-8.070276232, 1.607142923], [6.038476560, 10.43381031], [.495735214, 6.89\
3322855]];If one does not know how many points are contained in data, nops(data) give that number.nops(data);Here is the error functione:=(m,b,data)->sum(di(m,b,data[i][1],data[i][2]),i=1..nops(data));Before plotting, let us compute the slope and y-interceptwith(CurveFitting):LeastSquares(data,x);plot3d(e(m,b,data),m=-100..100,b=-100...100,style=patchcontour,axes=boxed);plot3d(e(m,b,data),m=-10..10,b=-30...30,style=patchcontour,axes=boxed);plot3d(e(m,b,data),m=0.8..1.14,b=4.5...6.5,style=patchcontour,axes=boxed,orientation=[0,0]);