The tidyverse prefers that your data be structured a certain way, and the data you have isn't quite there, but it's an easy fix. You have three variables (weekday, user type, and duration) and you should have one column holding each. This is easy to do with pivot_longer - I'll use a subset of your data to illustrate.
library(tidyverse)
df <- tribble(
~day_of_week, ~member, ~casual,
"Monday", 13.85, 30.4,
"Tuesday", 13.66, 27.9,
"Wednesday", 13.7, 27.1
)
df %>%
pivot_longer(c(member, casual), names_to = "type", values_to = "duration")
# A tibble: 6 × 3
day_of_week type duration
<chr> <chr> <dbl>
1 Monday member 13.8
2 Monday casual 30.4
3 Tuesday member 13.7
4 Tuesday casual 27.9
5 Wednesday member 13.7
6 Wednesday casual 27.1
Once you have that, a line plot will group observations into separate lines using the group aesthetic. In the code below, using type as the group means that all the observations with type "member" make up one line, and similarly with "casual".
df %>%
pivot_longer(c(member, casual), names_to = "type", values_to = "duration") %>%
ggplot(aes(day_of_week, duration, color = type, group = type)) +
geom_line()
Hope that helps!