Final answer:
The constant of proportionality is a constant factor that defines the linear relationship between two proportional variables, evident in equations such as Ohm's Law (V = IR) and the heat equation. It turns a proportional relationship into an equation and can be direct or inverse.
Step-by-step explanation:
The constant of proportionality in an equation is a constant factor that relates two variables that are proportional to each other. In other words, when one variable is a constant multiple of the other, this constant is the proportionality constant. For example, the equation V = IR describes Ohm’s Law, where V is the voltage, I is the current, and R is the resistance, which in this case is the constant of proportionality. Similarly, in the heat equation, the specific heat (C1) acts as the constant of proportionality, turning the proportionality into an equation that quantitatively describes the relationship between heat and temperature change.
The proportion can also refer to the specific mathematical relationship between quantities, which can be direct (x ∗ y) or inverse (a ∗ 1/b). When variables are directly proportional, their ratio is constant. If a variable is inversely proportional to another, their product is constant. Direct proportionality (P x T) means that the two variables increase or decrease together, while indirect proportionality (P x =) means one variable increases as the other decreases.