Quick answer
"Let up" is an intransitive verb phrase which is often translated as "amainar", and "slow down" is an intransitive verb phrase which is often translated as "reducir la velocidad". Learn more about the difference between "let up" and "slow down" below.
let up
An intransitive verb phrase is a phrase that combines a verb with a preposition or other particle and does not require a direct object (e.g. Everybody please stand up.).
intransitive verb phrase
1. (to become peaceful)
a. amainar
The storm finally began to let up after three days.Después de tres días, por fin la tormenta empezó a amainar.
b. mejorar
If the weather lets up, perhaps we can go outside and play.Si el tiempo mejora, quizás podamos salir a jugar.
2. (to back off)
a. cejar
The rebels in the caves refused to let up while there were still some of them alive.Los rebeldes en las cavernas se negaron a cejar mientras algunos de ellos seguían vivos.
b. desistir
Paco won't let up until he gets what he wants.Paco no desistirá hasta que consiga lo que quiere.
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slow down(
slo
 
daun
)
An intransitive verb phrase is a phrase that combines a verb with a preposition or other particle and does not require a direct object (e.g. Everybody please stand up.).
intransitive verb phrase
1. (to go slower)
a. reducir la velocidad
She tried to slow down, but it was too late to avoid the collision.Trató de reducir la velocidad, pero ya era tarde para evitar la colisión.
A transitive verb phrase is a phrase that combines a verb with a preposition or other particle and requires a direct object (e.g. Take out the trash.).
transitive verb phrase
2. (to delay)
a. retrasar
The accident at the factory has slowed down our production process.El accidente en la fábrica ha retrasado el proceso de producción.
b. hacer más lento
Too much multitasking while you're working can slow you down.Realizar demasiadas tareas a la vez puede hacerte más lento mientras estás trabajando.
3. (to make something go slower)
a. reducir la velocidad de (machine)
Slow down the car! We are in a school zone.¡Reduzca la velocidad del carro! Estamos en una zona de escuela.
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