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A transmission line with the characteristic impedance, Z0, not equal to the load impedance, ZL, works as an impedance transformer. A most popular example is a quarter-wave impedance transformer. In this case, the electrical length of the line is exactly lambda/4, and the input impedance of the line Zin is given by the equation Zin=Z0^2/ZL
In the figure, there are two types of loads (yellow dots), ZL=100 [ohm] and ZL=25 [ohm]. Notice that input impedance (red dots) of the line becomes either Zin=50^2/100=25 [ohm] or Zin=50^2/25=100 [ohm], respectively, as the line length approaches quarter wavelength.
