Find intersectionpoint between two functions

hello, i need to fund a exact intersection point between two functions on the X-axis. the script is following:

clear
close all
figure
hold on;
% 4,8 mil / vecka

years = 5;         
n = years*500;    % antalet mil
x = linspace(0,n,n+1);
Bpris = 16;     % bensin pris


%bil 1
k2 = Bpris*0.74;    % Bensin
a2 = 15000;    % Pris
b2 = years*392*12;    % Försäkring
m2 = a2+b2;
p2 = m2 + k2.*x;

%Bil 2
k3 = Bpris*0.55;    % Bensin
a3 = 22000;    % Pris
b3 = years*370*12;    % Försäkring
m3 = a3+b3;
p3 = m3 + k3.*x;

%plot(x,p1,"LineStyle","-")
plot(x,p2,"LineStyle","-")
plot(x,p3,"LineStyle","--")
xlabel('Körd sträcka [Mil]')
ylabel('Pris [Kr]')
hold off;

Now i have trubble making a code for intersection of the p2 and p3 functions (p2-p3=0) on the X-value, please help me.

Answer 1

[Star Strider]

Add this line just before the plot calls:

intx = (m2 - m3) / (k3 - k2);                       % X-Intersection

and add:

plot(intx, m3 + k3*intx, '+g', 'MarkerSize',20)

to the plot calls.

[Jurij Rudenson]

thanks!

[Jurij Rudenson]

but how do i make a line from the intersection to the Y-axis and from intersection to X-axis in the graph?

[Star Strider]

My pleasure!

Add this line to the plot calls:

plot([min(xlim) intx], [1 1]*(m3 + k3*intx), '--g',  [1 1]*intx, [min(ylim) (m3 + k3*intx)],'--g')

It will plot dashed green lines from the respective values for min(xlim) and min(ylim) to the intersection. (You did not mention originally that you wanted those lines, or I would have included the extra plot call in my Answer.)