Graph 1. Displacement versus time - velocity constant
The graph - displacement versus time, for motion with constant velocity, is a plot of the function
and this is the blue straight line in the Fig. 1.
The slope of this line
is the velocity v in this motion. The steeper this line, the higher the velocity.
The velocity is constant so the slope of the line representing this motion is constant too.
Notice, that the slope, formally
is not a dimensionless quantity as a tangent in trigonometry. If you measure the magnitude of an angle α on Fig.1 with a protractor and calculate its tangent on the calculator, the result will be not the velocity v. The velocity as a slope is defined by Eq. 2.
If you change the scale on the graph in Fig.1 you will change the “geometrical” slope of the blue line, but the velocity which may be determined from the graph with a new scale will be the same.
Fig.2 Plot from Fig.1 but with different scale on time axis.
To not become confused with the “tangent”, which is not a “trigonometrical tangent”, it is better to remember only the part of Eq. 2