Minkowski Diagram: Clarifying One-Dimensional Question

[Jarwulf]

I need a clarification about this diagram

On a one dimensional line two objects are riding along on the t and t' axis.

One present moment of black's is represented by the red line. Since the green segment defined from the origin to the red line is longer than the black segment defined from the origin to the red line wouldn't that mean from black's pov time for green is moving faster?

Also why do people multiply c to t for these diagrams? If you wanted a 45 degree angle for light wouldn't you just use t/c assuming you used meters for the x axis?

 

[Nabeshin]

Also why do people multiply c to t for these diagrams? If you wanted a 45 degree angle for light wouldn't you just use t/c assuming you used meters for the x axis?

To make the dimensions match. The x-axis has dimensions of length, and so does ct (for example in SI, m/s * s = m).