We don't really need all that code to answer the question. It would be much more preferable to just post some sample data. Anyway, I've tried to replicate your data as follows:
x=linspace(-8,8,9);
y=[linspace(0.5,0.28,4) linspace(0.29,0.59,5)];
Where x and y correspond to the data in alfa,machcriticosuperiore.
You could use a linear fit to the "two lines" and then solve for the point of intersection as follows:
idx=x<=-1;
l1=polyfit(x(idx),y(idx),1); % l1 is coefficient m, c, of a linear fit to the data
l2=polyfit(x(~idx),y(~idx),1);
xi=(l2(2)-l1(2))/(l1(1)-l2(1)); % When y of line 1 = y of line 2, you get xi=(c2-c1)/(m1-m2)
yi=l1(1)*xi+l1(2);
plot(x,y,'ok')
hold on, plot(xi,yi,'or')
You could also insert the intersection point into your original data and then plot with the line:
x=[x(idx) xi x(~idx)];
y=[y(idx) yi y(~idx)];
xlabel('\alpha'); ylabel('M_{cr_{sup}}');
plot(x,y,'-ok');
