If we use $(x_{\small{e}}, t_{\small{e}})$ for the event where the photon is emitted from
the torch, we can also write an equation to describe the photon that travels towards Amy
in Amy’s inertial frame (ie. a line with a gradient of -1, as shown in the above
visualisation):

For example, for the photon emitted at $(x_{\small{e}}, t_{\small{e}}) = (50, -50)$,
the photon will be defined by $x = -t$, so at $t = 0$, it’s at the origin. Try moving the
photon emission event to $(50, 0)$ in the visualisation above and check the equation
for the photon.

We now add Henry to the scene such that Henry is moving relative to Amy
at $v$ metres per second to the right (ie. along the x-axis in the positive
direction). We can write an equation that will tell us Henry’s position in
Amy’s inertial frame at any point in time:

Play with the visualisation below where $v=0.3c$ to demonstrate that according
to Amy, for every 10 seconds Henry moves 3 metres, or for every 50 seconds he
moves 15 metres.