subset-analogue removing fed in indexes?

Hello,

Here's my issue:

I want to plot the following vectors:

x <- c(0.0, 2.0, 15.0, 100.0, 105.0, 105.1, 110.0, 120.0, 120.1,

130.0)

data <- c(8.75, 8.75, 16.25, 38.75, 61.25, 8.75, NA, 8.75, NA, NA)

and avoid the line discontinuations caused by 'NA'.

plot_data <- na.omit(data)

will clean up 'data' for me, but now I need to get a 'plot_x' which
omits the values indexed with what's spit out by 'na.exclude(data)'.

Can anybody let me know a smooth way of how to delete entries with
certain indexes from a vector?