r - Plotting multiple lines from a data frame with ggplot2

Question

I am trying to plot multiple lines using ggplot2. My data is fitted into a data frame as follow:

> rs
  time           1           2           3           4
1  200 17230622635 17280401147 17296993985 17313586822
2  400 22328386154 22456712709 22499488227 22542263745
3  600 28958840968 29186097622 29261849840 29337602058
4  800 40251281810 40650094691 40783032318 40915969945
5 1000 73705771414 74612829244 74915181854 75217534464

I would like to use the "time" column as the x value. Other columns are y values of points in different lines. In the data above, there are 4 lines, each line consists of 5 points. More specifically, the first line has points (200, 17230622635), (400, 22328386154), (600, 28958840968), etc. The second line has points (200, 17280401147), (400, 22456712709), etc. (If you need further explanation of the data format, see P.S. in the end.)

To generate a similar data, you could use the following code:

rs = data.frame(seq(200, 1000, by=200), runif(5), runif(5), runif(5))
names(rs)=c("time", 1:3)

I followed some examples on stack overflow and tried to use reshape2 and ggplot2 to do this plot:

I first melt the data into a "long-format":

library('reshape2')
library('ggplot2')
melted = melt(rs, id.vars="time")

Then plot the data using the following statment:

ggplot() + geom_line(data=melted, aes(x="time", y="value", group="variable"))

However, I got an empty graph which has no point nor line.

Can anyone help me to see what's wrong with my procedure?

P.S.

About the data format:

You can imagine there are many students in the class and we have their scores of several quizzes. Each row contains one student's data: first column is the quiz number, then the rest of columns are his/her scores. For each student, we want to plot a line to reflect how his/her scores change over different quizzes, each point is the score of one quiz for a certain students. Since there are multiple students, we would like to draw multiple lines.

About the melted data:

Specific to the data I show above, the data I got from the melt() function is:

> melted
   time variable       value
1   200        1 17230622635
2   400        1 22328386154
3   600        1 28958840968
4   800        1 40251281810
5  1000        1 73705771414
6   200        2 17280401147
7   400        2 22456712709
8   600        2 29186097622
9   800        2 40650094691
10 1000        2 74612829244
11  200        3 17296993985
12  400        3 22499488227
13  600        3 29261849840
14  800        3 40783032318
15 1000        3 74915181854
16  200        4 17313586822
17  400        4 22542263745
18  600        4 29337602058
19  800        4 40915969945
20 1000        4 75217534464

Answer 1

Drop the quotes:

ggplot(data=melted, aes(x=time, y=value, group=variable)) + geom_line()

see: ggplot aesthetics