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Yes, you can.
Yes, intervals can be either on the Y Axis (Vertical), or the X Axis (Horizontal).
It does not have to. The independent variable, if there is any, usually goes on the x axis. Since time, particularly for time series, is often an independent variable, it goes on the x axis. However, if I were studying the time interval between the oldest and youngest sibling (brother or sister) in families of different size, I would plot the family size on the x axis and time on the y axis. In this case, the family size is the independent variable and the time [interval] the dependent.
a scale with diffrent numbers
title,axis,interval,label and scale