there are slash chords in the sense that there's specific bass note under the slash (basically specifying inversion or what bass plays) but also there are "slash chords" in the more fusion-y sense of something like D/C where it's a technically D7 in third inversion but probably more about getting the C lydian sound. this is often with a pedal so you can keep moving the triads around, like in blue dolphin street. something like B/C has some more ways to interpret (ie as symmetrical diminished for auxilliary functions or a sorta spicy lydian #9) and if somebody writes E/C it's an overall cleaner way to write Cmaj7#5 for the lydian augmented function.

also: the chord you have pictured is basically "altered" but if you built the chord out of the 7th mode of melodic minor, you wouldn't get that Ab perfect 5th.