I don't know of way to make geom_abline show only part of a line, but you could accomplish this with geom_segment and the gganimate package.
library(tidyverse); library(gganimate)
line_coords <- tribble(
~time, ~x, ~y, ~xend, ~yend,
0, -10, -10, -10, -10,
1, -10, -10, 10, 10
)
a <- ggplot(line_coords) +
geom_segment(aes(x = x, y = y, xend = xend, yend = yend)) +
scale_x_continuous(limits = c(-10,10)) +
scale_y_continuous(limits = c(-10,10)) +
transition_time(time) +
ease_aes("cubic-in-out")
animate(a, nframes = 60, fps = 20)