Lines in gnuplot can come in different styles; solid lines, dashed lines, or dotted lines, for example. Probably the easiest way to set these is to use the dashtype pattern specifier, in gnuplot 5 and above. The gnuplot help guide says:
set term pdfcairo font "Chalkduster,15"
set out 'dashes.pdf'
set key samplen 12 opaque box
PI = acos(-1.)
set xrange [0:2*PI]
plot sin(x) dashtype '-' lw 3 t 'Sin(x)', \
sin(2*x) dashtype '.' lw 3 t 'Sin(2x)', \
sin(3*x) dashtype '. - _' lw 3 t 'Sin(3x)', \
0 not
dashtype "pattern" # string containing a combination of the characters
# dot (.) hyphen (-) underscore(_) and space.
and some examples are shown below:
set term pdfcairo font "Chalkduster,15"
set out 'dashes.pdf'
set key samplen 12 opaque box
PI = acos(-1.)
set xrange [0:2*PI]
plot sin(x) dashtype '-' lw 3 t 'Sin(x)', \
sin(2*x) dashtype '.' lw 3 t 'Sin(2x)', \
sin(3*x) dashtype '. - _' lw 3 t 'Sin(3x)', \
0 not
Here we set up a pdf output, with a somewhat silly choice of font -- and one that I checked existed on my system. I set up the key to include a very long length line in the legend, because I am making up an example with a complicated dash type.
The plot line plots the functions sin(nx), n=1,2,3 and assigns each a different dash type: '-', '.' and '. - _'for dashes, dots, and a more complicated pattern. The results are shown below: