MATLAB: How to find an intersection between two lines on a plot

plot intersects

I have this code,
for P = [0; 1000; 2000; 6000; 10000; 12000; 12900; 13400; 13600; 13800; 14000; 14400; 15200; 16800; 18400; 20000; 22400];
Elon = [0; 0.0002; 0.0006; 0.0019; 0.0033; 0.0039; 0.0043; 0.0047; 0.0054; 0.0063; 0.0090; 0.0102; 0.0130; 0.0230; 0.0336; 0.0507; 0.1108];
d = 0.505;
r = d/2;
Area = pi*r^2;
GL = 2;
Stress = P/Area
Strain = Elon/GL
plot(Strain,Stress,'-x')
axis([0 0.06 0 120000]);
grid;
grid minor;
title('Stress vs. Strain')
xlabel('Strain')
ylabel('Stress, psi')
hold on;
text(0.00195,5.991e+04,'\leftarrow Proportional limit');
Proprtinal_limit = Stress(6)
E = (Stress(6)-Stress(1))./(Strain(6)-Strain(1))
refline(E,-30724)
axis([0 0.06 0 120000]);
end
I need to find the X and Y coordinates for the intersection of "Plot" and "refline".

Best Answer

Try this: 
RL = Strain*E -30724;                               % ‘refline’ As Funciton Of ‘Strain’ 
D = RL - Stress;                                    % Difference
[Du,ix] = unique(D, 'stable');                      % Unique ‘D’ & Indices
IntsctX = interp1(D(ix), Strain(ix), 0)             % Value Of ‘Strain’ At Intersection
IntsctY = E*IntsctX - 30724                         % Value Of ‘Stress’ At Intersection
producing: 
IntsctX =
       0.00324479065349119
IntsctY =
          68968.0850755092
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