Question

I have plotted a graph in matlab with:

plot(x,y)

and my graph has different slopes, how do i draw tangents on each slope and calculate the coefficient for the slope?

Answer 1

If you don’t have an explicit function for the plotted points, you can use finite differences for estimating the derivative. The following is appropriate for points not on the border of the data span:

plot(x,y);
hold all;

% first sort the points, so x is monotonically rising
[x, sortidx] = sort(x);
y = y(sortidx);

% this is the x point for which you want to compute the slope
xslope = (x(1)+x(end))/2;

idx_a = find(x<xslope,1,'last');
idx_b = find(x>xslope,1,'first');
% or even simpler:
idx_b = idx_a+1;
% this assumes min(x)<xslope<max(x)

xa = x(idx_a);
xb = x(idx_b);
slope = (y(idx_b) - y(idx_a))/(xb - xa);

Now drawing that slope, it depends on what you want: just a short line:

yslope = interp1(x,y,xslope);
ya_sloped = yslope + (xa-xslope)*slope;
yb_sloped = yslope + (xb-xslope)*slope;
line([xa;xb],[ya_sloped;yb_sloped]);

or a longer line

yslope = interp1(x,y,xslope);
xa = xa + 4*(xa-xslope);
xb = xb + 4*(xb-xslope);
ya_sloped = yslope + (xa-xslope)*slope;
yb_sloped = yslope + (xb-xslope)*slope;
line([xa;xb],[ya_sloped;yb_sloped]);

I’m pretty sure there’re no bugs in this code, but I’ll test it out when I have matlab around 😉