arbitrary point with the know slope to another line to specify point on that second line

I have two lines, one of them is operating line and the other is equilibrium line. I need to specify an arbitary point on a operating line, then with the known slope I need to draw a line that stops on the equilibrium line and obtain the point on equlibrium line. How can I achieve that?

I need it for separation process course to find interface mole fraction

[Sam Chak]

Could you try sketching out the lines? This helps to visualize.

[Ceren Ecemsu Varan]

I was able draw the lines that I have chosen but after this part i don't know how to stop them at the blue line, which will correspond to the values that I want

[Sam Chak]

From what you have now, please indicate or mark on the figure which one is operation and the other is equilibrium, as well as the points where you want the lines to end.

[Sam Chak]

OK I guess you want to find the intersections between multicolored lines and the thick blue line. Right?

If so, can you provide the parameters of line equation?

y = m*x + c

[Ceren Ecemsu Varan]

the main red line is operating line

the main blue line is equilibrium line

and I want to know the points that end on the blue line for that 10 interface line

Answer 1

[Sam Chak]

Hi @Ceren Ecemsu Varan

Since you are unable to provide additional info, perhaps you can do something like this:

% Analysis
x1 = linspace(0, 14e-3, 1401);
y1 = 220/7*x1;                      % blue line
x2 = linspace(0, 5e-3, 501);
y2 = 64*x2 + 0.03;                  % red line
plot(x1, y1, 'LineWidth', 1.5), hold on,
plot(x2, y2, 'LineWidth', 1.5)
x3 = linspace(2.5e-3, 5e-3, 251);
y3 = 0.28 - 36*x3;                  % orange line
plot(x3, y3, 'LineWidth', 1.5), hold off, axis([-3/1000 15/1000 -0.25 0.55]), grid on

% find intersection between orange line and blue line
f1 = @(x) 0.28 - 36*x - 220/7*x;
x0 = 4/1000;            % initial guess (near the intersection)
interX = fzero(f1, x0)

interX = 0.0042

% New Plot
x4 = linspace(2.5e-3, interX, 251);
y3 = 0.28 - 36*x4;
plot(x1, y1, 'LineWidth', 1.5), hold on,
plot(x2, y2, 'LineWidth', 1.5)
plot(x4, y3, 'LineWidth', 1.5), hold off, axis([-3/1000 15/1000 -0.25 0.55]), grid on