It's always a good idea to store time or datetime information as Pandas datetime datatype.
In your example, if you only want to keep the time information:
df['time'] = (df.x + 6) * pd.Timedelta(1, unit='h')
Output
x y1 y2 y3 time
0 0 -0.523190 1.681115 11.194223 06:00:00
1 1 -1.050002 1.727412 13.360231 07:00:00
2 2 0.284060 4.909793 11.377206 08:00:00
3 3 0.960851 2.702884 14.054678 09:00:00
4 4 -0.392999 5.507870 15.594092 10:00:00
5 5 -0.999188 5.581492 15.942648 11:00:00
6 6 -0.555095 6.139786 17.808850 12:00:00
7 7 -0.074643 7.963490 18.486967 13:00:00
8 8 0.445099 7.301115 19.005115 14:00:00
9 9 -0.214138 9.194626 20.432349 15:00:00
If you have a starting date:
start_date='2018-07-29' # change this date appropriately
df['datetime'] = pd.to_datetime(start_date) + (df.x + 6) * pd.Timedelta(1, unit='h')
Output
x y1 y2 y3 time datetime
0 0 -0.523190 1.681115 11.194223 06:00:00 2018-07-29 06:00:00
1 1 -1.050002 1.727412 13.360231 07:00:00 2018-07-29 07:00:00
2 2 0.284060 4.909793 11.377206 08:00:00 2018-07-29 08:00:00
3 3 0.960851 2.702884 14.054678 09:00:00 2018-07-29 09:00:00
4 4 -0.392999 5.507870 15.594092 10:00:00 2018-07-29 10:00:00
5 5 -0.999188 5.581492 15.942648 11:00:00 2018-07-29 11:00:00
6 6 -0.555095 6.139786 17.808850 12:00:00 2018-07-29 12:00:00
7 7 -0.074643 7.963490 18.486967 13:00:00 2018-07-29 13:00:00
8 8 0.445099 7.301115 19.005115 14:00:00 2018-07-29 14:00:00
9 9 -0.214138 9.194626 20.432349 15:00:00 2018-07-29 15:00:00
Now the time / datetime column have a special datatype:
print(df.dtypes)
Out[5]:
x int32
y1 float64
y2 float64
y3 float64
time timedelta64[ns]
datetime datetime64[ns]
dtype: object
Which have a lot of nice properties, including automatic string formatting which you will find very useful in later parts of your projects.
Finally, to plot using matplotlib:
# multiple line plot
plt.plot( df.datetime.dt.hour, df['y1'], marker='o', markerfacecolor='blue', markersize=12, color='skyblue', linewidth=4)
plt.plot( df.datetime.dt.hour, df['y2'], marker='', color='olive', linewidth=2)
plt.plot( df.datetime.dt.hour, df['y3'], marker='', color='olive', linewidth=2, linestyle='dashed', label="y3")
plt.legend()
plt.show()