Here is one way:
x = 0:0.05:1; % define data
y = sin(x).^2;
x1 = x(10); % define interval
x2 = x(20);
xrange = x(find(x == x1):find(x == x2)); % pick out x and y vals in interval
yrange = y(find(x == x1):find(x == x2));
p = polyfit(xrange, yrange, 1); % do linear curve fit
yfit = polyval(p, xrange);
figure
hold on; grid; box
plot(x,y,xrange,yfit,'-r')
The first element of p is the slope of the linear curve.
