what are the basis functions for the linear interpolating polynomial p\(x) = c\x + c2? in matlab

In MATLAB, we can use the built-in function polyfit to find the coefficients c1 and c2 of the linear interpolating polynomial p(x) = c1*x + c2.

Here's an example code to find the coefficients for some sample data:

main.m
% Sample data
x = [1, 2, 3, 4];
y = [2, 4, 1, 3];

% Find the coefficients
coefs = polyfit(x, y, 1);

% Display the coefficients
disp(['c1 = ' num2str(coefs(1)) ', c2 = ' num2str(coefs(2))]);
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The output will be something like:

main.m
c1 = 0.16667, c2 = 2.5
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So the basis functions for this linear interpolating polynomial are:

main.m
p(x) = 0.16667*x + 2.5
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