how would i find the intersection of a line with an graph of unknown equation or data points in matlab

One way to find the intersection of a line with a graph of unknown equation or data points in MATLAB is by using the intersect function. The intersect function finds the intersection of two curves given their X and Y data points. Here's an example:

main.m
% Generate some sample data
x = linspace(-10, 10, 100);
y = sin(x);

% Define your line
m = 0.5; % Slope
b = 1; % y-intercept
lineX = [-5, 5]; % Range of X values for line
lineY = m*lineX + b; % Calculate Y values for line

% Plot the graph and the line
plot(x, y)
hold on
plot(lineX, lineY)

% Find the intersection
[xi, yi] = intersect(x, y, lineX, lineY);
plot(xi, yi, 'ro')
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In this example, we generate some sample data for the graph and define a line with a slope of 0.5 and a y-intercept of 1. We then use the intersect function to find the intersection between the graph and the line. Finally, we plot the intersection point as a red circle.

Note that if the line and the graph do not intersect, the intersect function will return empty arrays. In this case, you can either adjust the range of the line or find a different method to find the intersection.