Final answer:
The property of equality shown is the Multiplicative Property of Equality, which allows multiplication of both sides of an equation by the same nonzero number while maintaining the equality.
Step-by-step explanation:
If (m = n), then (-\frac{3}{4}m = -\frac{3}{4}n). The property of equality illustrated here is the Multiplicative Property of Equality. This property states that if you multiply both sides of an equation by the same nonzero number, the two sides remain equal. In this case, both sides of the equation m = n are being multiplied by -\frac{3}{4}, and as a result, we have -\frac{3}{4}m = -\frac{3}{4}n.
The Multiplicative Property of Equality is essential because it allows us to manipulate equations while maintaining their balance. Other properties of equality, such as the Reflexive Property, the Symmetric Property, and the Transitive Property, also play integral roles in solving equations but are not depicted in this particular scenario.