I found this picture from a physics stack exchange question on time dilation: Time dilation all messed up!
I am now returning to it a few weeks later and was wondering if I am correctly interpreting what the diagram is showing, as I seem to run into a slight issue.
When the moving observer reads 11 o clock on his wrist watch that corresponds with a line through space time parallel to the x' line, such that all events on that line appear to simultaneously occur at 11 o clock for him. In this case, the event of the stationary observer at x = 0, reading 9 o clock on his wrist watch lies on the t' = 11 o clock line for the moving observer.
My question is, what would happen if the stationary observer was at x = 1 or basically just closer to the moving observer, when he reads t' = 11 o clock. From the diagram it appears as though this means that the line (t'=11) cuts the t axis further up (later on in the stationary observers time). But according to the equation $t′=γt$. There should be no position dependence, the moving observer should only see one time on the stationary observers clock regardless of how close or far he is.
Where have I gone wrong?