effect of area on the pressure of a liquid

was in a lesson and the teacher gave this talk which i was following until the end.

If a fluid flows in a pipe which has one point of entry and one point of exit the mass flow rate in = mass flow rate out.

due to law of conservation of mass. therefore we get the following equation

p(1)A(1)v(1) = p(2)A(2)v(2)

because liquids are incompressible the density is constant whatever the pressure therefore

A(1)v(1) = A(2)v(2)

fluid travels fastest through the narrowest sections.

therefore indicating individual particles accelerate.

according to Newtons second law, the forces on the particles must therefore be unbalanced.

**This implies the pressure is lowest at the narrowest points**

i don't understand how he derived the part in bold. can someone explain how this link was made, thanks