How is the voltage and current plot for a matched transmission line constant?
When there is an impedance change in (or at the end of) a transmission line, energy is reflected from the point of the change, resulting in a flow of energy in both directions from that point.

These two flows are summed at every point along the line, sometimes adding to each other, and sometimes partially or wholly cancelling out. The relative phase between the two flows is determined by the distance from the discontinuity.

When there is no discontinuity, there is no reflected energy, so the voltage and current levels measured at every point along the line are the same.