# Interpretation of Fixed Interaction Effects in a Linear Mixed Model

I have a linear mixed model for predicting speed of a street crossing by a pedestrian with the factors VS (vehicle speed), GAP (selected time gap size for crossing), the interaction factors VSxGAP and a random intercept.

How can I interpret parameter estimates for the interaction effects?

I only have a random effect of the intercept - is it still correct to interpret the interaction effects as follows?:

a) At the reference VS of 60km/h, pedestrians reduce their speed by 80mm/s with increasing GAP by 1 GAP-unit.
b) Pedestrians reduce their speed by |-80+70|=10mm/s with increasing GAP at VS 30km/h - interaction effect 30km/h x GAP
c) Pedestrians reduce their speed by |-80+10|=70mm/s with increasing GAP at VS 50km/h - interaction effect 50km/h x GAP

And how can I interpret the fixed effects for VS categories 30km/h and 50km/h? Would it be correct to say:
d) The crossing speed level (mean) or intercept is lowered by 600mm/s for 30km/h
e) The crossing speed level (mean) or intercept is lowered by 60mm/s for 50km/h

And is it correct to imagine the plots for each VS to have different slopes due to the interaction effect!?
The fact that I have not determined any random effects, except for the intercept, confuses me a lot with the interpretation of the estimates - so I would be very thankful for responses.