\line ¶Synopsis:
\line(x_run,y_rise){travel}
Draw a line. It slopes such that it vertically rises y_rise for every horizontal x_run. The travel is the total horizontal change—it is not the length of the vector, it is the change in x. In the special case of vertical lines, where (x_run,y_rise)=(0,1), the travel gives the change in y.
This draws a line starting at coordinates (1,3).
\put(1,3){\line(2,5){4}}
For every over 2, this line will go up 5. Because travel specifies that this goes over 4, it must go up 10. Thus its endpoint is (1,3)+(4,10)=(5,13). In particular, note that travel=4 is not the length of the line, it is the change in x.
The arguments x_run and y_rise are integers that can be
positive, negative, or zero. (If both are 0 then LaTeX treats the
second as 1.) With
\put(x_init,y_init){\line(x_run,y_rise){travel}},
if x_run is negative then the line’s ending point has a first
coordinate that is less than x_init. If y_rise is negative
then the line’s ending point has a second coordinate that is less than
y_init.
If travel is negative then you get LaTeX Error: Bad \line or
\vector argument.
Standard LaTeX can only draw lines with a limited range of slopes
because these lines are made by putting together line segments from
pre-made fonts. The two numbers x_run and y_rise must have
integer values from −6 through 6. Also, they must be
relatively prime, so that (x_run,y_rise) can be (2,1) but not
(4,2) (if you choose the latter then instead of lines you get sequences
of arrowheads; the solution is to switch to the former). To get lines
of arbitrary slope and plenty of other shapes in a system like
picture, see the package pict2e
(https://ctan.org/pkg/pict2e). Another solution
is to use a full-featured graphics system such as TikZ, PSTricks,
MetaPost, or Asymptote.