Non-liniar function. Why is that?

Hi! I'm new here, and i think I have a little problem. How it is possible to divide two liniar functions and get a non liniar function. Check the code below!

if true
  % t1 = [0:0.1:60];
t2 = [60:0.1:90];
t3 = [90:0.1:110];
t4 = [110:0.1:140];
f1 = 10*ones(size(t1)) + t1/2;
f2 = 40*ones(size(t2));
f3 = 40*ones(size(t3))-2*(t3-90*ones(size(t3)));
f4 = 30*sin(pi*(t4-110*ones(size(t4)))/30);
t = [t1 t2 t3 t4];
f = [f1 f2 f3 f4];
m1 = 20*ones(size(t));
a1 = f./m1;
m2 = 5*ones(size(t)) + 15*ones(size(t)) - 0.03*t;
a2 = f./m2;
m3 = 5*ones(size(t)) + 15*ones(size(t)) - 0.5*t;
m3(m3<=5)=5;
a3 = f./m3;
plot(t,f,t,m3,t,a3);
grid on;
end

Answer 1

[Image Analyst]

Why should it be? It's like (20-0.5*x)/(10+0.5*x). That's not linear in x. The numerator and denominator are, individually , but the ratio is not. Why do you think it should be?