How to find point of intersection of lines given y value

i have the following code, i am trying to find where the line y = 1000 intersects with each line

l = 5000;
x1 = [0 290];
x2 = [22 233];
x3 = [60 190];
x4 = [80 300];
x5 = [100 439];
x6 = [150 384];
y = [0 l];
 
%space time graph
plot(x1,y, 'DisplayName' ,'vehicle 1' )
hold on 
plot(x2,y, 'DisplayName' ,'vehicle 2')  
plot(x3,y, 'DisplayName' ,'vehicle 3') 
plot(x4,y, 'DisplayName' ,'vehicle 4') 
plot(x5,y, 'DisplayName' ,'vehicle 5') 
plot(x6,y, 'DisplayName' ,'vehicle 6')
hold off
 
% Add title and axis labels
title('Time - Space graph')
xlabel('Time (seconds)')
ylabel('Distance (meters)')
lgd = legend;
lgd.NumColumns = 2;
 
y1 = yline(1000);

how would i find the corresponding x values when it intersects with each line

Answer 1

[Adam Danz]

For each line,

1) Compute the slope of the line using the standard slope forumula.

m = (y(2)-y(1)) / (x(2)-x(1)); 

2) Compute the y-intercpet of each line using

b = y(1)-m*x(1); 

3) Now you have the equation of the line and you just need to solve for x at y=1000

x = (1000 - b) / m; 

To show the intersection:

yline(1000)
xline(x)

Answer 2

[Star Strider]

Try this:

l = 5000;
x1 = [0 290];
x2 = [22 233];
x3 = [60 190];
x4 = [80 300];
x5 = [100 439];
x6 = [150 384];
y = [0 l];

xm = [x1; x2; x3; x4; x5; x6];
yl = 1000;
for k = 1:size(xm,1)
    B = [xm(k,:); 1 1].' \ y(:);
    lines(k,:) = [xm(k,:); 1 1].' * B;
    xint(k) = (yl - B(2)) / B(1);
end

%space time graph
figure
hold on
y1 = yline(1000);
for k = 1:size(xm,1)
hv(k) = plot(xm(k,:), y, '-', 'DisplayName', sprintf('vehicle %d',k));
plot(xint(k), yl, '+k');
end
hold off
grid

% Add title and axis labels
title('Time - Space graph')
xlabel('Time (seconds)')
ylabel('Distance (meters)')
lgd = legend(hv, 'Location','SE');
lgd.NumColumns = 2;

producing:

.